EDUCATION  DEFT* 


A  TEXT  BOOK 


OP 


NATURAL   PHILOSOPHY: 


ACCURATE,  MODERN,  AND  SYSTEMATIC 


EXPLANATION   01    '£l 


ELEMENTARY  PRINCIPLES  OF  THE  SCIENCE. 


ADAPTED   TO   USE  IN 

HIGH  SCHOOLS  AND  ACADEMIES. 

WITH    149   ILLUSTRATIONS. 

BY  LE  BOY  C.  COOLEY,  PH.  D., 

// 

PBOFESSOB     OF     NATURAL     SCIENCE    IN     VA8SAR     COLLEGE. 

•' Let  science,  by  cultivating  man's  Intellect,  elevate  him  to  nobler  ana  more  spirit;*) 
rle^s  of  God's  wisdom  and  power."— Cooke. 


NEW  YORK: 
SCRIBNER,    ARMSTRONG     &    CO., 


Q 


Uttered  accenting  to  act  of  Congress,  in  £he  year  IStt,  ty 

LE  BOY  C.  COOLEY, 

AV  the  Clerk's  Office  of  tne  District  Court  of  the  United  State*  for  tOs 
Northern  District  of  New  York. 

EDUCATION  DEFT. 


TROW'S 
PRINTING  AND  BOOKBINDING  Co.. 

PRINTERS   AND    STEREOTYPERS, 

205-213  Kast  \-2tli  St.) 

NEW    VORK. 


TOPICS   FOR   REVIEW, 


PAET   I. 

THE  PHENOMENA  OF  MATTER  AT  REST. 


INTRODUCTION. 

The  Properties  of  Matter. — (1.)  Properties  of  matter — Extension — Im- 
penetrability— Indestructibility — Elasticity.  (2.)  Physical  Propertie§— 
Chemical  Properties.  (3.)  Natural  Philosophy. 

CHAPTER    I. 

§  1.  The  Fundamental  Ideas. — (4.)  Molecule — Inertia — Attraction — 
Repulsion.  These  four  ideas  explain  the  phenomena  of  nature. 

§  2.  Varieties  of  Attraction.— (5.)  I.  Gravitation  —  Universal  —  Th« 
first  law — The  second  law.  II.  Cohesion — Its  power — Through  in- 
sensible distances.  III.  Adhesion.  IV.  Capillary  Force  —  Causes 
liquids  to  penetrate  porous  solids — The  first  law — The  second  law. — 
(6.)  These  varieties  of  attraction  are  but  different  manifestations  of  a 
single  influence — Problems. 

CHAPTER    II. 

OP  THE  PHYSICAL   FORMS  OF  MATTER. 

Introduction. — (7.)  Application  of  the  fundamental  ideas. 
§  1.    Of  the    Characteristic    Properties    of   Solids.— (8.)   Hardne 
Tenacity — Malleability — Ductility — Crystalline  Form. 


M69893 


iv  TOPICS    FOR    REVIEW. 

§  2.  Of  1he  Characteristic  Properties  of  Liquids. — (9.)  Attraction  arid 
repulsion  nearly  equal — Mobility. 

§  3  Of  Liquids  at  Rest  (10.)  Pressure  equal  in  all  directions — 
Surface  is  level — The  level  surface  is  convex.  (11.)  "Water  in  pipei 
rises  as  high  as  its  source — The  supply  of  water  to  cities—  Springs — 
Artesian  wells.  (12.)  Pressure  independent  of  the  shape  of  the  vessel — 
It  depends  on  the  depth  of  the  liquid — To  calculate  the  pressure. — 
(13.)  Bodies  immersed  are  pressed  upward — With  force  equal  to  the 
weight  of  fluid  displaced — The  solid  lighter  than  water — The  solid 
heavier  than  water.  (14.)  Specific  gravity — I.  Of  gases — II.  Of  liquids 
— By  direct  weighing — By  the  hydrometer — By  the  use  of  a  bulb — II L 
Of  solids — Heavier  than  water — Lighter  than  water — Table.  (15.)  The 
equal  transmission  of  pressure — The  shape  of  the  vessel  makes  no  dif- 
ference— The  hydrostatic  press — Problems. 

§  4.  Of  the  Properties  of  Gases. — (1 6.)  Compressibility — Expansibility 
—Elasticity — Weight. 

§  5.  Of  the  Pressure  of  the  Atmosphere. — (17.)  The  atmosphere  exerta 
pressure  in  all  directions  about  151bs.  to  the  square  inch.  (18.)  I.  The 
barometer  shows  the  pressure  of  the  atmosphere — The  pressure  of 
atmosphere  depends  upon  its  weight — Upon  the  amount  of  water- 
vapor  it  contains — Upon  the  elasticity  of  its  lower  portions.  II.  The 
Common  Pump.  III.  The  Forcing  Pump.  IV.  The  Siphon. 

§  6.  Of  the  Relation  between  Volume  and  Weight.— (19.)  The  volume 
of  a  given  weight  of  air  depends  upon  pressure  and  temperature — I. 
Pressure — Volume  inversely  as  tbe  pressure — Density  of  the  atmos- 
phere— Is  greatest  at  the  surface  of  the  earth.  II.  Temperature — Heat 
increases  the  volume  of  air  ^Q  of  its  bulk  for  each  degree — Problems. 


PAET    II. 

THE  PHEXOHEXA  OF  MATTER  IX  MOTION 

CHAPTER    III. 


OF  MOTION. 


Introduction. — (20.)  Application  of  the  fundamental  ideas. 
§  1.  Of  Motion  caused  by  a  Singk  Force.— (2  L)  The  first  law  of  motion 
—The  second  law— The  third  law.     (22.)  Velocity— Uniform  velocity- 


T  0  F  i  0  to     if  u  rt,     R  K  V  l  &  VV  .  v 

Impulsive  force — Uniform  velocity  produced  by  an  impulsive  force — 
Space  equals  time  multiplied  by  velocity.  (23.)  A  constant  force — 
Uniformly  accelerated  velocity — Difficulties  in  the  way  of  experiment 
— Overcome  by  Atwood's  machine.  (24.)  Experiments  with  Atwood'a 
.machine — Proof  of  first  principle — Proof  of  second  principle — Analysis 
of  the  motion  of  a  falling  body — Construction  of  the  table — From  the 
table  obtain  the  laws — From  the  table  obtain  the  formulas — By  the 
formulas  solve  problems — Problems. 

§  2.  Motion  caused  by  more  than  one  Force. — (25.)  If  a  body  be 
acted  on  by  two  forces  represented  by  the  sides  of  a  parallelogram, 
they  are  equivalent  to  a  single  force — The  resultant  may  be  found. — 
(26.)  Any  force  may  be  resolved — To  find  the  component  which  acts  in 
a  given  direction.  (27.)  Two  forces  in  the  same  direction — The  point 
of  application — The  weight  of  a  body — The  center  of  gravity.  (28.) 
Curved  motion — Is  produced  by  at  least  two  forces — One  of  which  is 
constant — Projectiles — Their  motion  due  to  two  forces. 

§  3.  The  Indestructibility  of  Force. — (29.)  Force  is  indestructible- 
Motion  can  not  cease  without  exerting  the  same  amount  of  force  which 
produced  it — Suppose  a  body  move  without  resistance,  Momentum — 
Motion  due  to  an  impulse  meets  with  resistance — Suppose  a  constant 
."orce  applied  to  overcome  resistance,  Living  Force. 

§  4.  Of  Machinery. — (30.)  The  principle  of  momentum — Machines — 
Simple — The  law  of  equilibrium.  (31.)  Levers — Three  classes — Appli- 
cation of  the  principle  of  momentum — the  compound  lever — Application 
of  the  lever.  (32.)  The  wheel  and  axle — Acts  on  the  principle  of  the 
lever — Application  of  the  principle  of  momentum — One  wheel  may  turn 
another  by  means  of  cogs — By  friction — By  bands — Application  of  the 
wheel  and  axle.  (33.)  The  pulley — Fixed  and  movable — The  principle 
of  momentum  to  the  fixed  pulley — To  the  movable  pulley  with  one 
rope — To  the  movable  pulleys  with  separate  ropes — Applications  of  the 
pulley.  (34.)  The  inclined  plane — If  the  power  act  parallel  to  the 
length  of  the  plane — If  it  act  parallel  to  the  base  of  the  plane — Applica- 
tions of  the  inclined  plane.  (35.)  The  wedge.  (36.)  The  screw — 
Application  of  the  principle  of  momentum — Applications  of  the  screw—- 
Problems. 

§  5.  Of  the  Motion  of  Liquids.— .(37.)  The  velocity  of  a  jet  of  water  the 
wane  as  that  of  a  falling  body — The  velocity  depends  upon  the  depth 
of  the  orifice— Calculated  by  the  formula  Y=  2  «7Sy.  (38.)  To  calculate 
the  quantity.  (39.)  The  velocity  less  than  the  theory  gives — The 
quantity  less  than  the  tneory  gives — Quantity  increased  by  using  tubes. 


Vi  TOPICS    FOR    REVIEW. 

(4C.)  The  undershot  wheel — The  overshot  wheel — The  hreas*  \vh«eir-  • 
The  American  turbine. 

§  6.   Of  the  Motion  of  Air.— (41.)  Wind— The  trade  winds— Due  to 
heat  and  the  rotation  of  the  earth. 


CHAPTER    IT 

OP    MOTION. —  VIBRATIONS. 

Introduction. — (42.)  Application  of  the  fundamental  ideas. 

§  1.  Of  Vibrations  of  the  Pendulum.— {43.)  The  pendulum— Y^rater 
under  the  influence  of  gravitation  and  inertia — The  first  law — The 
second  law — The  third  law.  (44.)  The  center  of  oscillation — The  laws 
apply  to  this  point.  (45.)  The  pendulum  is  used  to  measure  time — To 
determine  the  form  of  the  earth. 

§  2.  Of  Vibrations  of  Cords. — (46.)  The  vibration  of  cords — Due  to 
elasticity  and  inertia — The  laws  of  vibration — first,  second,  third. — 
(47.)  Progressive  vibrations — The  motion  appears  to  be  lengthwise  of  the 
tube — Ventral  segments.  (48.)  The  cord  vibrates  as  a  whole — In 
ventral  segments  at  the  same  time. 

§  3.  Of  Vibrations  of  Liquids  and  Gases. — (49.)  Water  waves — May 
interfere.  (50.)  The  vibrations  of  air — Alternate  rarefactions  and  con- 
densations— In  all  directions — Different  sets  interfere. 

%  4.  Of  Vibrations  of  Mokcuks. — (51.)  Molecules  in  motion — Moleculaf 
vibrations  affect  our  senses. 

CHAPTER    V. 

OF  THE  EFFECTS  OF  VIBRATIONS. — I.   SOUND. 

§  1.  The  Origin  and  Transmission  of  Sound. — (52.)  Sound  produced 
by  vibrations.  (53.)  Sound  waves — Are  transmitted  through  all  elastic 
bodies — "With  different  velocity  in  different  media — The  first  law — The 
second  law — With  uniform  velocity  in  the  same  medium. 

§  2.  Of  Refraction  and  Reflection  of  Sound. — (54.)  Sound  waves  pasg 
from  one  medium  to  another — Refraction — Sound  made  louder  by  re- 
fraction. (55.)  The  reflection  of  sound — The  law — The  echo. 

§  3.  Of  Musical  Sounds. — (56.)  Musical  Sounds — Any  noise  repeated 
rapidly  causes  a  continuous  sound — Puffs  of  air  made  rapidly  give  a 
musical  sound.  (57.)  Musical  sounds  differ — I.  Pitch — Pitch  depend! 


TOPICS    FOR    REVIEW.  ^ 

on  rapidity  of  vibration — Intervals — The  diatonic  scale—  The  number 
of  vibrations  for  the  notes.  II.  Intensity.  III.  Quality. — (58)  Musi- 
cal  instruments — Stringed  instruments — Pitch  raised  by  using  strings 
of  different  lengths — Of  different  tension — Of  different  weight. 

CHAPTER    VI. 

OF   THE    EFFECTS   OF  VIBRATIONS. II.    LIGHT. 

§  1  Of  the  Nature  of  Light,  and  the  Laws  of  its  Transmission.  (59.) 
Light  is  the  effect  of  vibrations — The  ether — Luminous  bodies.  (60.) 
Rays  of  light— Are  transmitted— In  straight  lines— With  uniform  velocity 
— Its  intensity  inversely  aa  the  square  of  the  distance — Photometry. 

§  2.  Of  the  Reflection  of  Light.— (61.)  Reflection— The  law.  (62.) 
Mirrors — The  effect  of  plane  mirrors — The  effect  of  concave  mirrors — 
The  effect  of  convex  mirrors.  (63.)  Images  by  reflection — Image  of  a 
point  (64.)  Images  by  plane  mirrors.  (65.)  Images  by  concave  mir- 
rors—  The  image  of  a  point.  (66.)  Object  beyond  the  center  — 
Between  the  center  and  the  focus — Between  tLe  focus  and  the  mirror. 
(67.)  Images  by  convex  mirrors. 

§  3.   Of  the  Refraction  of  Light.— (68).  Refraction— The  first  law— Tne 
second  law.    (69.)  The  index  of  refraction.     (70.)  Lenses— The  effect 
of   convex  lenses — The  effect  of   concave  lenses.    (71.)  Images  are 
formed  by  convex  lenses — The  image  of  a  point.     (72.)  Object  at  twice 
the  focal  distance — Farther  away — At   a  less  distance — Between  the 
focus  and  the  lens.     (73.)  Images  by  concave  lenses. 
-v  §  4.   Of   the    Decomposition  of  Light. — (74.)  Prisms — Prisms   refract 
light — Prisms    decompose  light.     (75.)  The   black  lines  of   the  solar 
spectrum — The  bright  lines  in  spectra  of  artificial  light.     (76.)  Decompo- 
sition by  rain-drops — The  primary  rainbow — The  red  band  on  the  out 
side — The  colors  iu  the  form  of  an  arch — The  secondary  law.     (77.)  De 
composition  by  refraction — The  color  of  bodies — The  color  of  the  sky- 
The  color  of  the  clouds. 

§  5.  Of  Optical  Instruments. — (78.)  The  microscope — The  telescope- 
The  magic  lantern — The  camera  obscura — The  eye. 

CHAPTER    VII. 

THE  EFFECTS  OP  VIBRATIONS. — II L   HEAT. 

g  1.   Of  the  Sources  and  Nature  of  Heat. — (79.)  The  sources  of  heat- 


van  TOPICS    FOR    REVIEW. 

1.  The  heavenly  bodies — II.  Mechanical  action,  friction — III.  Cheun 
cal  action.  (80.)  The  material  theory — The  dynamic  theory. 

§  2.  Of  the  Transmission  of  Heat.~(8l.)  Rays  of  heat — Transmission 
of  heat  rays — Laws  of  transmission — Law  of  reflection — Law  of  refrac- 
tion. (82.)  The  diffusion  of  heat — I.  By  conduction — Through  solids^ 
Through  liquids — Through  gases.  II.  By  convection — Air  is  heated  in 
no  other  way — Liquids  are  heated  by  convection — JTo  convection  in 
solids.  III.  By  radiation — It  depends  upon  temperature — On  the 
nature  and  condition  of  the  surface.  ^ 

§  3.  Of  the  Effects  of  ffcat.—(83.)  The  action  of  heat  is  twofold— It 
raises  temperature  —  It  expands  bodies  —  Solids  —  Liquids  —  Gases — 
Temperature  is  measured  by  expansion — The  thermometer — Various 
forms.  (84.)  Temperature  indicates  the  rapidity  of  molecular  motion — 
Expansion  indicates  a  change  in  the  relative  position  of  molecules — 
Sensible  and  latent  heat — Specific  heat.  (85.)  At  the  melting  point 
—Temperature  stops  rising — But  the  expansion  increases.  (86.)  The 
boiling  point — Depends  on  the  purity  of  the  liquid — On  the  nature  of 
the  vessel — On  pressure — At  this  point  temperature  is  constant — But 
the  expansion  increases.  (87.)  Heat  is  required  to.  expand  a  body— 
The  same  amount  is  given  off  when  the  body  again  contracts. 

§  4.  Of  the  Steam- Engine.— (88.)  The  elastic  force  of  steam — The 
boiler — The  cylinder — The  crank — High  and  low-pressura  engines. 


CHAPTER     VIII. 

OF  ELECTRICITY. 

Introduction. — (89.)  Application  of  the  fundamental  ideas. 

§  1.  Of  Frictional  Electricity. — (90.)  Electricity  produced  by  friction — 
The  electrical  machine — Electricity  detected  by  electroscopes — Two 
opposite  forces — Measured  by  electrometers — The  first  law — The  second 
law.  (91.)  A  charged  body — A  non-conductor — An  insulated  body — A 
charged  body  polarizes  an  insulated  conductor.  (92.)  A  series  of  con- 
ductors polarized — The  theory  of  induction.  (93.)  The  Leyden-jar— -It 
may  be  charged — It  may  be  discharged — The  Leyden  battery.  (94.) 
The  electricity  of  the  atmosphere — Of  the  same  nature  as  frictional 
electricity — Lightning  is  the  discharge  of  oppositely  charged  clouds— 
The  aurora — Produced  by  electric  discharges.  (95.)  The  effect  of  points 
— Lightning-rods.  (96.)  The  mechanical  effects  of  electricity — Chemical 
effects — Physiological  effects. 


TOPICS    FOR    REVIEW.  fc 

§  2.  Of  Magnetic  Electricity. — (97.)  Magnets — Natural — Artificial — 
Different  forms — Their  force  strongest  at  the  ends.  (98.)  Attraction 
and  repulsion — The  law.  (99.)  A  magnet  will  polarize  a  bar  of  iron — 
Several  bars  in  succession — All  the  molecules  of  a  magnet  are  polarized. 
X100.)  A  bar  magnet  supported — "Will  point  north  and  south — Its 
variation — Annual  and  daily.  (101.)  The  dip  of  the  needle. 

§  3.  Of  Voltaic  Electricity.— (102.)  Voltaic  electricity— The  voltaic 
circuit — Grove's  battery — Bunsen's  battery.  (103.)  It  is  produced  by 
chemical  action — Resistance — Quantity  and  intensity — Quantity  depends 
on  the  size  of  the  plates — Intensity  depends  on  the  number  of  plates— 
(104.)  The  effects  of  electricity — Heat — Light — Magnetism,  the  electrif 
telegraph — Induction,  the  Ruhmkorf  coiL  (106.)  Conclusion, 


TO  THE  PUPIL. 


MY  DEAB  FRIEND: — 

THE  most  faithful  efforts  are  sometimes  followed  by  partial 
success,  or,  it  may  be,  utter  failure,  for  want  of  gome  proper 
method  of  study.  I  have  tried  to  systematize  the  principles  of 
Natural  Philosophy,  and  I  believe  that  if  you  reduce  your  efforts 
K)  a  corresponding  system,  you  will  find  the  acquisition  of  this 
science  less  difficult,  more  pleasant,  and  of  enduring  value. 

Let  me  suggest  the  following  plan.  First,  read  the  heading  of 
the  paragraph  (numbered  in  parenthesis)  that  you  may  know 
what  subject  the  paragraph  presents.  Then,  look  over  the  topics 
(numbered  without  parenthesis)  and  compare  them  with  the 
heading,  to  see  what  are  its  essential  thoughts.  After  this,  study 
each  topic  in  order;  and  finally,  learn  the  heading  and  see  that 
you  can  develop  its  topics  without  referring  to  the  book. 

Do  not  be  satisfied  with  the  statement  of  facts  alone  ;  but  care- 
fully study  the  relation  of  thoughts.  You  will  find  the  analyti- 
cal contents  valuable  for  this  purpose. 

Finally,  I  hope  you  will  not  regard  this  little  book  as  a  com- 
mentary on  the  subjects  it  treats.  You  will  find  it  profitable  to 
have  some  larger  work  at  hand  in  which  you  can  find  additional 
explanations  of  subjects  which  are  of  special  interest  to  you.  I 
have  not  aimed  to  exhaust  the  subject,  but  to  give  you  an  outline 
which,  by  present  study  or  future  reading,  you  will  be  able  to  fill. 

That  your  pleasure  in  this  study  shall  equal  that  which  I  have 
felt  while  instructing  so  many  classes  in  this  science,  is  the  desir* 
of  your  friend. 

L.  0.  0. 


PREFACE. 


THIS  volume  is  designed  to  be  a  text-book  of  natural  philosophy 
salted  to  the  wants  of  high  schools  and  academies. 

The  author  believes  that  the  following  features  of  his  work 
adapt  it  to  the  purpose  for  which  it  is  designed. 

1.  It  contains  no  more  than  can  be  mastered  by  average  classes 
in  the  time  usually  given  to  this  science.     To  this  end,  the  polar- 
ization of  light,  sounding  flames,  and  kindred  subjects  of  a  lesa 
elementary  nature,  are  omitted.     But  that  the  pupil  may  have 
access  to  such  important  and  interesting  matter,  an  appendix  has 
been  added. 

2.  It  presents  a  judicious  selection  of  subjects.     Omitting  what 
ever  is  merely  novel  or  amusing,  it  gives  a  plain  and  concise  dis- 
cussion of  elementary  principles,  of  theoretical  and  practical  value. 

3.  It  is  an  expression  of  modern  theories.     It  recognizes  the 
fact  that  the  spirit  of  a  new  philosophy  pervades  every  depart- 
ment of  science,  and  presents  the  doctrines  of  molecules  and  of 
molecular  motions,  instead  of  the  old  theory  of  imponderables, 
which  has  been  swept  away.     Carefully  avoiding  whatever  is  yet 
only  probable,  it  seizes  upon  what  has  come  to  be  universally 
accepted,  and,  as  far  as  may  be,  adapts  it  to  the  course  of  ele- 
mentary instruction  which  it  proposes. 

4.  It  is  logical  in  the  arrangement  and  development  of  sub- 
jects.    A  single  chain  of  thought  (see  Analytical  Contents)  binds 
the  different  branches  of  the  science  into  one  system  of  related 
principles. 

6.  It  is  thoroughly  systematized.     Chapters,  sections,  para- 


Xii  PREFACE. 

graphs,  anl  topics,  have  been  arranged  with  careful  regard,  on 
the  one  hand,  to  the  relation  of  principles  to  each  other,  and  on 
the  other  hand,  to  the  best  methods  of  conducting  the  exercises 
of  the  class-room. 

At  the  beginning  of  each  paragraph  is  a  plain  and  concise 
statement  of  useful  facts  and  principles,  while  the  paragraph  itself 
contains  the  discussion  of  them  by  topics  in  their  natural  order. 

The  mind  can  not  work  intelligently  unless  it  has  some  object 
toward  which  to  direct  its  efforts.  No  scientist  pursues  his 
researches  by  experiment,  without  first  proposing  some  fact,  or 
principle,  to  be  tested.  The  discoveries  of  the  immortal  Faraday 
were  drawn  from  experiments,  not  made  at  random,  but  con- 
ceived and  executed  to  test  the  truth  of  theories  proposed  in  his 
own  mind  beforehand.  (See  Faraday  as  a  Discoverer,  by  Tyn- 
dall).  The  synopsis,  at  the  beginning  of  each  paragraph  in  this 
volume,  gives  the  pupil  a  clear  idea  of  the  work  proposed  to  be 
done.  He  is  then  prepared  to  see  how  the  facts  of  observation 
may  be  used  to  establish  the  principles  of  physical  science. 

Moreover,  there  is  an  increasing  number  of  teachers  who 
believe  that  oral  instruction  is  quite  as  important  to  the  pupil  as 
the  study  of  a  text-book.  These  headings  of  the  paragraphs  are 
texts,  which,  taken  together,  give  a  compact  view  of  the  entire' 
science,  and  which  will  enable  the  teacher  to  freely  supplement 
the  discussions  of  the  book,  by  experimental  or  mathematical 
proofs.  To  facilitate  this  work, still  further,  references  have  been 
given  to  the  most  accessible  and  reliable  works  wherein  the 
subjects  of  the  text  are  more  exhaustively  treated.  The  works 
chiefly  referred  to,  are:  Silliman's  Physics,  Cooke's  Chemical 
Physics,  Atkinson's  Ganot's  Physics,  Tyndall's  Lecture*  on  Sound, 
and  Tyndall's  Heat  as  a  Mode  of  Motion.  No  teache*  of  Natural 
Philosophy  can  afford  to  be  without  these  books. 


ANALYTICAL   CONTENTS. 


PART   I.— THE   PHENOMENA   OF  REST. 

(1.)  The  qualities  of  matter  are  called  its  properties. 

v*.,  All  properties  of  matter  are  either  Physical  or  Chemical. 

(3.)  Natural  Philosophy  is  the  science  which  treats  of  the  physixt 

properties  of  matter. 

(4.)  The  FUNDAMENTAL  IDEAS  in  Natural  Philosophy  are  expressed  by 
the  words  molecule,  inertia,  attraction  and  repulsion. 

Attraction  is  called  gravitation,  cohesion,  adhesion,  and 
capillary  force,  according  to  the  circumstances  under 
which  it  acts. 

(T.)  Attraction  and  repulsion,  acting  upon  the  molecules  of  bodies,  produce 
the  three  physical  forms  of  matter :  solid,  liquid,  and  gaseous. 

The  characteristic  properties  of  solid  bodies  are  hard- 
ness, tenacity,  malleability,  ductility,  and  crystalline  form. 
The  characteristic  property  of  liquid  bodies  is  mobility. 
The  characteristic  properties    of  gaseous    bodies  are 
expansibility  and  compressibility. 

PART  II.— THE   PHENOMENA   OF  MOTION. 

(20.)  Read  (4)  and  (7).     Attraction  and  repulsion,  acting  upon  masses  of 
matter  determine  their  condition  of  rest  or  motion. 

Motion  is  uniform  if  produced  by  an  impulsive  force. 
Motion  is  uniformly  accelerated  if  produced  by  a  con- 
stant force. 

Motion  is  curved  if  produced  by  two  forces,  one,  at 
least,  of  which  is  a  constant  force. 


Xiv  ANALYTICAL     CONTENTS. 

The  force  which  causes  motion  will  be  reproduced  when 
the  motion  stops :  hence  the  principle  of  momentum. 

The  principle  of  momentum,  applied  to  any  one  of  the 
simple  machines,  will  determine  its  law  of  equilibrium. 

The  free  motion  of  liquid  bodies  is  due  to  the  attraction 
of  gravitation,  and  must  obey  the  laws  of  this  force. 

The  free  motion  of  air,  or  wind,  is  due  to  the  action  of 
heat 

(42.)  Read  (4),  (7),  and  (20).    Attraction,  repulsion,  and  inertia,  acting 
upon  masses,  or  upon  molecules,  produce  vibration — 

Of  the  pendulum. 

Of  cords. 

Of  liquids. 

Of  gases. 

Of  the  molecules  of  all  bodies. 

These  vibrations  of  molecules  affect  cor  organs  of  sense, 
and  give  rise  to  the  phenomena — 

Of  sound. 

Of  light. 

Of  heat. 

(i9.)  A  constant  and  opposite  action  of  attraction  and  repulsion  among 
the  mokcuks  of  bodies,  gives  rise  to  the  phenomena  of  electricity. 


PAET   I. 

JHE  PHENOMENA  OF  MATTER  AT  RESf 


NATURAL   PHILOSOPHY 


INTRODUCTION. 


THE    PROPERTIES    OF    MATTER. 

(1.)  THE  qualities  of  matter  are  usually  called  its 
properties.  Those  most  important  for  us  to  notice  in 
the  outset  are  Extension,  Impenetrability,  In^estructi- 
oility  and  Elasticity. 

1.  The  Properties  of  Matter. — In  what  respects  is  a 
block  of  granite  so  unlike  a  block   of  wood?     The 
granite  is  brittle,  it  may  be  chipped  with  a  chisel :  the 
wood  is  soft,  it  may  be  cut  with  a  knife.     The  granite 
is  heavy ;  to  lift  it  may  require  the  power  of  an  en- 
gine: the  wood  is  much  lighter;  perhaps  a  single  arm 
may  move  it.     We  are  thus  able  to  perceive  a  differ- 
ence in  bodies  only  because  there  is  a  difference  in  the 
qualities  they    possess.     These    qualities    are    called 
properties. 

2.  ^tension. —  Every    body    of   matter,    however 
small,  fills  a  portion  of  space.     It  is  not  possible  to 
think  of  a  body   which   should  have   no   size.     This 
property   of  matter,  by   virtue  of  which  it   occupies 
space,  is  called  extension. 


18  NATURAL    PHILOSOPHY 

3.  Impenetrability. — Not  only  do  all  bodies  occupy 
space,  every  body  fills  the  space  assigned  it  to  the  ex- 
clusion of  all  others.     One  body  may  not  be  pushed 
into  the  substance  of  another  ;  it  can  take  the  place  of 
another   only  when  the  other  has  been  thrust  away. 
When,   for    example,    a    nail    is    driven   into    wood, 
it  pushes  the, .p&.rtfclos  of  wood  out  of  its  way;  and 
when  the  hand  is  plunged  into  water,  the  water  is 
Irhru&t  agi^fc-  to  give: it  place.     This  property  of  matter, 
by  virtue  of  which  no  two  bodies  can  fill  the  same 
space  at  the  same  time,  is  called  impenetrability. 

4.  Indestructibility. — A  piece  of  gold  may  be  cut 
into  parts  so  small  as  to  be  almost  invisible.     It  may 
be  dissolved  by  acids  and  made  to  disappear,  or  by  in- 
tense heat  it  may  be  changed  into  thin  vapor,  and  hid 
in  the  air.     After  all  these  changes  have  been  wrought 
upon  the  gold,  its  particles  may  be  again  collected  to 
form  a  mass  like  the  original  one  without  the  slightest 
diminution  in  weight.     Amid  all  the  changes  which 
we  witness  in  the  forms  and  qualities  of  bodies,  not  a 
single  atom  is  destroyed.     This  property  of  matter,  by 
virtue  of  which  no  particle  can  be  destroyed,  is  called 
indestructibility. 

5.  Elasticity. — When  an  india  rubber  ball  is  pressed 
in  the  hand  it  is  made  smaller,  but  the  moment  the 
pressure  is  removed  the  ball  springs  back  to  its  original 
size.     The  same  quality  is  possessed  in  various  degrees 
by  all  bodies.     In  such  as  lead  and  clay  it  is   very 
slight,  yet  a  ball  made  of  either  of  these  substances 
will  spring  back  after  having  been  for  a  moment  com- 
pressed.    On  the  other  hand,  an  ivory  ball,  when  let 
fall  upon  a  marble  slab,  rebounds  nearly  to  the  height 
from  which  it  fell,  showing  that  the  power  of  restitu 


NATURAL    PHILOSOPHY.  19 

tion  is,  in  this  case,  almost  equal  to  the  force  of  com- 
pression. This  property  of  matter,  by  virtue  of  which 
it  restores  itself  to  its  former  condition  after  having 
yielded  to  some  force,  is  called  elasticity. 

This  property  of  matter  is  more  universal  than  ia 
commonly  supposed.  Glass,  although  very  brittle,  ia 
highly  elastic.  A  glass  ball  will  rs  5/9)131  d,  from  a  marble 
slab  almost  as  well  as  one  of  jvbry/  „  Steel  is  likewise 
hard  and  brittle,  yet  the  U>amt^ciis:  ;syorflJ,ricj&J3T'  JLHJ 
bent  double  without  breaking. 

But  should  we  attempt  to  describe  all  the  properties 
of  matter  in  detail,  the  time  given  to  the  study  of  our 
science  would  be  filled  with  little  else.  The  suc- 
cess of  a  student  of  nature  depends  largely  upon  his 
power  to  classify  phenomena,  and  to  study  them  in 
groups. 

(2.)  All  the  properties  of  matter  may  be  grouped  in 
two  divisions,  viz. :  physical  properties,  of  which  mallea- 
bility and  ductility  are  examples  ;  and  chemical  prop- 
erties, such  as  combustibility  and  explosibility. 

1.  Physical  Properties. — Many  of  the  metals  may 
be  reduced  to  thin  plates,  or  leaves,  by  hammering  them. 
Zinc  is  a  familiar  illustration,  sheets  of  this  metal  being 
often  placed  under  stoves,  to  protect  the  floor  from 
heat.  This  property  is  called  malleability.  Gold  is 
eminently  malleable  :  it  may  be  beaten  into  leaves  so 
thin,  that  a  pile  of  eighteen  hundred  of  them  would  be 
no  thicker  than  a  sheet  of  common  paper. 

Many  substances 'may  be  also  drawn  into  wire.  Iron, 
copper,  and  brass  wires  are  sufficiently  familiar.  The 
peculiar  property  by  virtue  of  which  they  may  be 
drawn  into  wire  is  called  ductility.  Glass,  when  heated 


20  NATURAL    PHILOSOPHY. 

to  a  bright  red  heat,  is  remarkably  ductile.  If  a  point, 
pulled  out  from  the  mass,  be  fastened  to  the  circum- 
ference of  a  turning  wheel,  a  uniform  thread  as  fine  as 
the  finest  silk  may  be  wound  at  the  rate  of  a  thousand 
yards  an  hour. 

JSTow  fix  the  attention  upon  the  fact  that  the  wonder- 
ful malleability  c-f:  gojdf  and  the  surprising  ductility  of 
glass,  are  shown  without, (my  change  in  the  nature  of 
ffit&\$ffijsfy&^e&\ « .Thei-gold  is  the  same  material  in  the 
form  of  leaf  as  it  was  before  it  manifested  its  malle- 
ability. The  glass  in  the  form  of  thread  is  the  identical 
substance  which,  by  being  drawn,  manifested  its  duc- 
tility. All  properties  which,  like  these,  a  body  may 
manifest  without  undergoing  any  change  in  its  nature, 
are  called  physical  properties.  If  now  we  examine 
those  properties  described  in  the  early  part  of  this  sec- 
tion, we  will  find  them  all  to  belong  to  this  group. 
Extension,  impenetrability,  and  the  rest,  are  proper- 
ties which  a  body  may  show  without  any  change  in  its 
natme. 

2.  Chemical  Properties. — "Wood,  by  burning,  shows 
that  it  is  combustible.  ISTo  substance  can  manifest  the 
property  of  combustibility  except  by  actually  taking 
fire,  and  when  it  burns  it  changes  to  something  else. 

Who,  not  already  familiar  with  gunpowder,  would 
suspect  it  to  be  so  violently  explosive  ?  It  can  show 
that  it  is  explosive,  only  by  ceasing  to  be  gunpowder, 
and  becoming  a  mass  of  vapor.  Properties  like  these, 
which  a  body  can  not  manifest  without  changing  its 
nature,  are  callsd  chemical  properties. 

This  classification  of  properties  helps  us  to  define 
accurately  the  science  whose  elements  we  are  beginning 
to  study. 


NATURAL     PHILOSOPHY,  21 

(3.)  Natural  Philosophy  is  the  science  which  treats  of 
the  physical  properties  of  matter,  and  of  those  phenom- 
ena in  which  there  is  no  change  in  the  nature  of  bodies. 

If  now  we  look  out  upon  the  phenomena  which 
nature  presents,  and  will  apply  the  test  furnished  by 
this  definition,  we  may  select,  from  among  the  multi- 
tude, those  which  it  is  the  province  of  this  science  to 
explain.  Thus,  for  example,  we  see  the  vapors  rise; 
we  see  the  rain  drops  fall.  We  listen  with  delight  to 
the  harmonies  of  music,  and  derive  exquisite  pleasure 
from  the  colors  of  the  rainbow.  In  these  phenomena, 
and  in  numerous  others  easily  recognized  by  an  atten- 
tive mind,  we  can  detect  changes  in  the  form  and 
place  of  bodies,  but  none  whatever  in  their  nature. 
But  if  we  regard  the  more  quiet,  yet  not  less  imposing 
phenomena  of  the  seasons,  we  may  discover  a  multitude 
whose  discussion  is,  by  the  definition,  excluded  from 
this  science.  The  young  verdure  of  the  spring-time 
changes  at  length  to  the  matured  foliage  and  ripening 
grains  of  summer.  The  fruits  and  hues  of  autumn, 
more  somber,  except  where  enlivened  by  the  richly 
colored  ripening  leaves  of  the  maple  or  the  oak,  soon 
afterward  appear,  only  to  be  in  turn  displaced  by  the 
crisp  and  crackling  snows  of  winter.  These  events  are 
brought  about  by  changes  gradually  taking  place  in 
the  nature  of  substances,  and  the  explanation  of  all 
such  phenomena  must  be  reserved  for  the  science  of 
chemistry. 


22  NATURAL    PHILOSOPHY. 


CHAPTEK    I. 


§  1.    THE   FUNDAMENTAL   IDEAS. 

(4)  THE  fundamental  ideas  in  natural  philosophy 
are  expressed  by  the  words  molecule,  inertia,  attraction 
and  repulsion.  These  four  ideas,  when  fully  under- 
stood, will  furnish  the  explanations  of  nearly  all  the 
phenomena  of  which  the  science  treats. 

1.  The  Molecule. — A  molecule  is  a  particle  of  matter 
which  can  not  be  divided  without  changing  its  nature. 
All  bodies  are  made  up  of  such  particles.  A  piece  of 
marble  may  be  crushed  and  powdered  until  its  par- 
ticles are  like  the  finest  dust,  yet,  when  seen  through  a 
microscope,  they  appear  like  angular  blocks  of  stone, 
and  may  be  still  further,  divided.  The  same  is  true  of 
a  piece  of  ice.  If  its  temperature  be  kept  low  enough 
while  it  is  being  crushed,  every  particle  of  the  ice- 
powder  will  still  be  a  block  of  ice.  By  applying  heat, 
the  little  block  is  first  melted,  and  then  changed  to 
steam,  which  show?  that  it  was  composed  of  innumer- 
able smaller  pieces.  How  minute  must  be  the  par 
tides  thus  made  absolutely  invisible !  Yet  each  one 
is  a  fragment  of  the  original  block  of  ice.  The  heat 
has  not  changed  their  nature.  The  identical  particles 
which  make  up  the  steam,  composed  the  drop  of  water 


NATURAL    PHILOSOPHY.  23 

and  the  little  piece  of  ice.  But  it  is  thought  that  these 
particles  can  not  be  divided  without  changing  their 
nature,  and  they  are  called  molecules. 

All  bodies  are  made  up  of  molecules.  The  size  of 
a  body  depends  upon  their  number ;  its  shape,  upon 
their  arrangement. 

"Whenever  the  term  molecule  is  used,  it  should  con« 
vey  this  idea,  that  every  body  of  matter  is  made  up  of 
a  multitude  of  little  particles,  which  do  not  touch  each 
other,  and  which  can  not  be  divided  without  changing 
their  nature. 

2.  Inertia. — A  heavy  wheel  requires  force  to  put  it 
in  motion,  or  when  in  motion  it  requires  force  to  stop 
it.     It  has  no  power  to  change  its  own  condition.     At 
rest,  it  would  rest  forever  if  left  to  itself;  or  once  in 
motion  it  would  forever  move,  unless  acted  upon  by 
some  force  beyond  itself.     This  idea,  that  no  material 
body  has  power  to  change  its  own  condition  of  rest  or 
motion,  is  expressed  by  the  term  inertia. 

3.  Attraction. — When  a  body  is   not  supported  it 
falls  to  the  ground.     This  familiar  event  illustrates  the 
tendency  of  bodies  to  approach  each  other.     Moreover, 
we  have  seen  that  bodies  are  composed  of  molecules, 
BO  small  that  the  most  powerful  microscope  can  not 
reveal  them,  yet  we  must  think  of  each  as  a  separate 
body  as  truly  as  though   the  eye  could  measure  its 
diameter.      Now,  by   what  influence   are   they  held 
together  ?     It  is  doubtless  the  same  invisible  force  by 
which  a  body  is  drawn  to  the  earth  when   not  sup- 
ported.    It   is   a  fact  that  all  bodies,  however  large 
or  small,  have   a  tendency   to  approach  each   other. 
The  force  which   causes  this  tendency  is  called  at- 
traction,. 


24  NATURAL    PHILOSOPHY. 

4.  Repulsion. — If  a  ball  of  India  rubber  be  pressed 
in  the  hand   it   is   made   smaller — its   molecules   are 
brought  nearer  together.     When  the  pressure  is  re 
moved  they  instantly  spring  to  their  former  position. 
While   springing    back   the   molecules   are   evidently 
being  thrust  away  from  each  other. 

Or  try  the  following  experiment.  Suspend  a  pith 
ball,  or  a  little  ball  of  cotton,  by  a  fine  silk  thread : 
briskly  rub  a  warm  dry  lamp  chimney  with  a  woolen 
cloth  :  bring  the  ball  and  glass  together  for  a  moment, 
after  which  it  will  be  found  that  the  ball  will  fly  away 
from  the  glass,  and  show  so  strong  an  aversion  to  it 
that  they  can  not  be  brought  together.  The  force  un- 
der whose  influence  bodies  tend  to  separate  is  called 
repulsion. 

The  action  of  repulsion  among  molecules  is  more  uni- 
versal than  among  masses.  It  is  illustrated  by  many 
familiar  facts.  If,  for  example,  a  bladder  be  filled  with 
cold  air,  and  then  heated,  it  will  burst.  Repulsion 
drives  the  molecules  of  air  apart,  and  pushes  them 
through  the  bladder.  "When  a  drop  of  water  is  heated 
it  becomes  steam,  and  fills  a  space  about  1700  times 
larger  than  before. 

5.  These  Four  Ideas. — Out  of  these  four  ideas  may 
be  drawn  the  explanation  of  almost  all  the  phenomena 
which  take  place  in  nature.     A  great  city,  with  all  its 
various  forms  of  architecture  and  machinery,  is  built  of 
a  few  familiar  substances,  such  as  wood,  and  iron,  and 
stone.   This  fact  may  excite  our  admiration  of  the  intel- 
ligence and  skill  of  man.  What,  then,  must  be  our  feel- 
ings when  we  discover  that  these  four  simple  ideas  are 
the  elements  out  of  which  the  sublime  fabric  of  the 
universe  has  arisen!      The  whole  system  of  material 


NATURAL    PHILOSOPHY.  2ft 

thirds  is  simple  and  orderly,  displaying  the  infinite 
knowledge,  power,  and  skill  of  a  divine  Architect. 

§  2.    VARIETIES  OF  ATTRACTION. 

(5.)  Attraction  receives  different  names  according  to 
the  circumstances  under  which  it  acts.  Gravitation, 
Cohesion,  Adhesion,  and  Capillary  Force,  are  its  most 
common  forms. 

I. GRAVITATION. 

A.  — Gravitation  is  that  form  of  attraction  which  is 
exerted  upon  all  bodies,  and  throughout  all  distances. 
It  is  governed  by  two  laws : — 

1st.  Its  force  is  in  proportion  to  the  quantity  of  mat- 
ter in  the  body  exerting  it. 

2d.  Its  force  is  inversely  proportional  to  the  square 
of  the  distance  through  which  it  acts. 

1.  Gravitation  is  universal. — All  bodies  are  under 
the  influence  of  gravitation.     The  leaf,  the  fruit,  the 
snow-flake,  fall  to  the  ground  because  they  are  attract 
ed  thither  by  gravitation.     They  press  upon  its  surface 
because  the  same  force  continues  to  act  after  they  reach 
the  earth.     No  distance  can  outreach  it,  for  it  is  the 
bond  which  holds  the  heavenly  bodies  in  their  orbits. 
JS"or  c'an  any  substance  cut  it  off,  or  even  diminish  its 
action ;  for  if  the  earth  should  come  between  the  sun 
and  moon,  these  two  bodies  would   attract  each  other 
with  the  same  degree  of  force. 

We  come  now  to  the  interesting  thought  that  this 
force  acts  with  infinite  regularity  and  precision. 

2.  The  first  law  of  gravitation. — To  illustrate  this 
law,  let  us  suppose  two  bodies,  one  containing  twice  aa 

a 


26  NATURAL    PHILOSOPHY. 

much  matter  as  the  other,  to  attract  a  third.  The  force 
exerted  by  the  first,  will  be  twice  as  great  as  that  by 
the  other.  If  one  body  weigh  nine  tons  and  another 
three  tons,  then  a  third  body  equally  distant  from 
them  will,  according  to  the  same  law,  receive  three 
times  as  much  attraction  from  the  first  as  from  the 
second. 

3.  The  second  law  of  gravitation. — To  illustrate  this 
law,  suppose  a  body  to  be  twice  as  far  from  the  center, 
or  source  of  attraction,  at  one  time  as  at  another.  In 
the  first  position,  the  attraction  will  be  only  one-fourth 
as  strong  as  in  the  second.  If  the  distance  be  three 
times  as  great,  the  force  will  be  one-ninth  as"  strong. 
If  two  distances  are  as  3  :  4:,  the  attractions  will  be  to 
each  other  as  16  :  9. 

Now,  the  weight  of  a  body  is  due  to  the  attraction 
of  gravitation.  Weight  must,  therefore,  increase  or 
diminish  in  exact  accordance  with  the  laws  of  gravitation 
The  greater  the  distance  from  the  earth,  the  less  will  a 
body  weigh.  Now,  distance  from  the  earth  is  measured 
from  its  center.  Wlten  on  the  surface  of  the  earth,  a 
body  is  4,000  miles  from  the  center;  suppose  it  were 
possible  to  carry  the  body  to  a  height  of  4,000  miles 
above  the  surface,  its  distance  from  the  center  would  be 
doubled^  and  its  weight  would  be  reduced  to  one-fourth. 

n. — COHESION. 

B. — Cohesion  is  that  form  of  attraction  which  acts 
between  the  molecules  of  the  same  body.  Its  power  is 
very  great,  but  only  through  insensibly  small  distances. 

1.  Cohesion. — Cohesive  attraction  holds  the  mole- 
/uies  of  a  body  together,  and  enables  it  to  keep  its  form 


NATURAL    PHILOSOPHY.  27 

and  size.  A  cubical  block  of  wood  remains  a  cube 
only  because  its  molecules  are  held  together  by  this 
force.  Were  it  not  for  its  action,  all  bodies  would  at 
once  dissolve  into  their  ultimate  molecules,  and  vanish. 

2.  Its  power. — The  strength  of  cohesion  is  often  very 
great.     The  molecules  of  a  piece  of  iron  are  so  strongly 
bound  by  it,  that  a  weight  of  500  Ibs.  may  be  lifted  by 
means  of  a  wire  one-tenth  of  an  inch  in   diameter. 
Even  a  strip  of  paper  is  not  easily  broken  by  a  force 
acting  exactly  in  the  direction  of  its  length. 

3.  It  acts   through  insensible  distances. — The   dis- 
tance through  which  cohesion  can  act  is  quite  too  small 
to  be  measured.     Let  the  parts  of  a  body  be  separated, 
and  the  strength  of  the  giant  is  gone. 

When  a  body  is  broken  its  parts  can  be  made  to 
cohere  again  only  with  great  difficulty.  In  a  few  soft 
bodies,  like  wax,  a  slight  pressure  will  force  the  molecules 
near  enough  together  tor  cohesion  to  take  hold  of  them  ; 
in  others  the  pressure  required  is  much  greater,  while 
in  the  majority  of  substances  it  is  so  great  as  to  bo 
practically  impossible. 

The  smith  unites  two  pieces  of  iron  by  welding.  Ho 
softens  the  iron  by  heat,  then  puts  the  two  pieces  to- 
gether and  unites  them  by  the  heavy  blows  of  his  sledge. 
Now,  what  he  does  is  simply  to  push  the  yielding  mole- 
cules of  the  two  pieces  of  iron  into  very  close  contact ; 
this  done,  cohesion  grasps  them,  and  the  two  pieces 
become  one. 

m. ADHESION. 

C. — Adhesion  is  that  form  of  attraction  which  acts 
between  molecules  of  different  bodies  without  changing 
their  nature. 


28  NATURAL    PHILOSOPHY. 

If,  for  example,  the  hand  be  plunged  into  water  it 
comes  out  covered  with  a  thin  film  of  the  fluid  ;  it  may 
be  immersed  in  alcohol  with  the  same  effect.  In  these 
cases  the  fluids  are  held  to  the  hand  by  adhesion.  The 
hand  may  be  withdrawn  from  a  bath  of  mercury  with- 
out retaining  a  particle  of  that  substance,  because  the 
adhesion  is  too  feeble  to  lift  the  fluid. 

This  force,  like  cohesion,  acts  only  through  distances 
too  small  to  be  measured :  unlike  cohesion  it  acts 
between  molecules  of  different  kinds  of  matter.  The 
value  of  glue  and  cement  is  due  to  the  powerful  adhe- 
sion which  acts  between  them  and  the  surfaces  of  solid 
bodies  which  they  bind  together. 

J 

IV. CAPILLARY   FORCE. 

D. — Capillary  Force  is  the  adhesion  of  a  liquid  to  a 
solid  which  is  partly  immersed  in  it.  It  generally 
causes  an  elevation  or  a  depression  of  the  liquid  along  the 
sides  of  the  solid.  It  also  causes  a  liquid  to  penetrate 
a  porous  solid.  It  is  governed  by  two  laws : — 

1st.  The  heights  to  which  a  liquid  rises  in  different 
tubes  of  the  same  material  are  inversely  proportional 
to  the  diameters  of  the  tubes. 

2d.  The  height  to  which  a  liquid  rises  between  par- 
allel plates  is  one-half  the  distance  it  will  rise  in  a 
tube  whose  diameter  is  equal  to  the  distance  between 
the  plates. 

1.  Capillary  Force.  —If  small  glass  tubes  be  inserted  in 
a  vessel  of  water,  it  will  be  seen  that  the  fluid  instantly 
springs  upward  and  remains  at  rest  in  the  tubes  con- 
siderably above  its  general  level.  (See  Fig.  1.)  Along 


NATURAL    PHILOSOPHY.  29 

the  outside  surface  of  the  tubes  the  water  also  climba 
to  a  little  height.  Fig.  i.  Fig.  a. 

If  tubes  be  inserted  in 
a  vessel  of  mercury,  this 
fluid  will  be  pushed  down. 
(Fig  2.)  The  mercury  in- 
side the  tubes  will  be  con- 
siderably below  the  gen- 
eral level,  while  the  fluid  against  the  outside  is  also 
depressed.  Here  are  two  well  marked  cases  of  capil- 
lary action. 

]$Tow,  when  a  piece  of  glass  is  plunged  into  water  it 
comes  out  wet,  but  when  plunged  into  mercury  it 
comes  out  as  free  from  the  liquid  as  when  it  entered 
and  by  repeated  experiments  it  is  shown  that  all  liquids 
which  will  wet  the  sides  of  the  tube  wiil  be  lifted^ 
while  those  which  will  not,  will  be  pushed  down. 

2.  It  causes  liquids  to  penetrate  porous  solids. — • 
An  easy  experiment  strikingly  illustrates  this  action. 
Take  a  common  bottle,  eight  or  ten  inches  high,  and 
wrap  it  in  a  sheet  of  white  blotting-paper,  whose  edges 
must  be  secured  by  a  bit  of  wax.  Place  the  bottle, 
now  prepared,  upon  a  dinner-plate.  Pour  water  upon 
the  plate  to  cover  the  lower  edge  of  the  paper,  and  im- 
mediately the  fluid  will  be  seen  rapidly  climbing  the 
sides  of  the  bottle,  which  it  will  not  cease  to  do  until 
it  has  reached  the  top.  The  beauty  of  the  experiment 
is  enhanced  by  filling  the  bottle  with  some  highly  colored 
liquid. 

The  rise  of  the  water  is  due  to  the  attraction  he 
tween  its  particles  and  those  of  the  paper  and  glass. 
This  force,  acting  downward  from  each  particle  of  the 
paper  through  the  definite  but  imperceptible  distance 


30  NATURAL    PHILOSOPHY. 

to  the  one  below  it,  lifts  a  particle  of  water.  The  next 
particle  of  paper  above,  then  lifts  it  higher.  Indeed, 
the  successive  particles  of  paper  upward,  are  the  success- 
ive steps  of  a  ladder,  up  which  the  water  is  impelled 
by  capillary  force. 

Numerous  familiar  facts  are  explained  by  this  experi- 
ment. Oil  is  carried  up  the  lamp  wick  to  supply 
the  flame  with  fuel.  By  a  similar  action,  water  is  dis- 
tributed through  loose  soils  to  keep  them  moist  and 
fertile.  So,  too,  in  a  great  degree,  the  sap  of  plants  and 
trees  is  carried  to  their  summits,  and  even  in  the  animal 
system  the  circulation  of  blood  through  the  minute 
blood-vessels  is  materially  aided  by  capillary  action. 

3.  The  first  law. — In  figure  1,  the  water  is  repre- 
sented as  being  lifted  to  different  heights  in  the  dif- 
ferent tubes.     The   height  to   which   any  fluid  ri^ea 
depends  upon  the  size  of  the  tube.     If  the  diameter  of 
one  tube  be  just  one-half  that  of  another,  water  will 
invariably  rise  in  it  twice  as  far.     If  the  diameters  of 
two  tubes  have  the  ratio  of  4 :  3,  then  the  water  will 
rise  in  them  to  heights  whose  ratio  is  3 :  4.     Or,  in 
other  words,  the  heights  are  inversely  as  the  diameters 
of  the  tubes. 

4.  The  second  law. — If  a  plate  of  glass  be  inserted 
in  water  the  liquid  will  rise  a  little  distance  against 
its    sides.     If   two    parallel  plates  be  inserted  near 
together,  the  water  will  rise   between  them,  and  by 
varying  their  distance  from  each  other  it  may  be  shown 
that  the  height  to  which  the  liquid  rises  is  inversely 
proportional  to  the  distance  between  the  plates. 

But  if  we  compare  the  elevations  which  take  place 
between  the  plates  with  the  height  to  which  the  same 
liquid  rises  in  tubes  whose  diameters  are  equal  to  the 


NATURAL    PHILOSOPHY.  31 

distance  between  the  plates,  we  discover  that  in  all 
cases  it  is  just  one-half. 

(6.)  We  need  not  suppose  that  gravitation,  cohesion, 
adhesion,  and  capillary  force  are  so  many  different 
kinds  of  force.  They  should  be  regarded  as  but  dif- 
ferent manifestations  of  a  single  influence. 

One  can  not,  it  would  seem,  study  the  phenomena 
thus  far  briefly  sketched  without  being  impressed  with 
the  variety  of  the  phases  and  effects  of  attraction,  yet 
we  do  well  to  regard  all  these  varied  effects  as  but  the 
different  ways  in  which  a  single  influence  manifests 
itself.  The  differences  between  gravitation,  cohesion, 
and  the  other  forms  of  attraction  that  have  been  named, 
are  apparent,  not  real.  When  bodies  are  separated  by 
sensible  distances,  the  attraction  between  them  is  called 
gravitation,  without  regard  to  their  size ;  but  when  the 
bodies  become  very  small,  and  the  distances  very  minute, 
the  force  is  called  cohesion.  Does  distance  alone,  then, 
change  the  nature  of  attraction  ?  Where  shall  the  Kne 
be  drawn  at  which  the  change  occurs  ?  Equally  unreal 
"are  the  differences  between  the  other  members  of  this 
group  of  forces,  so  that,  looking  behind  the  veil  of  ap- 
pearances, we  are,  upon  the  very  threshold  of  science, 
permitted  to  catch  a  glimpse  of  the  sublime  simplicity 
which  everywhere  reigns  in  the  works  of  nature,  and 
which  it  is  the  glory  of  scientific  study  to  reveal. 

But  shall  we  ask  what  is  this  single  power  whose 
effects  are  so  varied  and  imposing?  We  name  it 
attraction.  Who  need  inquire  further?  The  little 
bird  that  vainly  beats  his  head  against  the  cage  bars, 
affords  a  warning  to  the  man  of  science  who  would 
attempt  to  search  for  this,  which  God  has  hidden. 


32  NATURAL    PHILOSOPHY. 

PROBLEMS  ILLUSTRATING  THE  LAWS  OF  ATTRACTION. 

1.  With  how  many  times  greater  force  will  a  body 
be  attracted  by  a  mass  of  iron  ^weighing  9"  tons,  than 
by  a  block  of  stone  weighing  3^' tons,  when  both  are 
at  the  same  distance  from  it?  >  Ans.  3. 

2.  Two  lead  balls,  one  weighing  5  ozs.  and  the  other 
12  ozs.,  are  hanging   at  a  distance   of  10  ft.   from   a 
third;  what  relative  degrees  of  force  do   they  exert 
upon  it? 

f  3.  One  jb^all  of  lead  attracts  another  through  a  dis- 
tance of  16 ft.,  with  a  force  of  olDa.;  what  force  would 

it  exert  if  placed  at  a  distance  of  $0  ft  ?    Ans.  2  Ibs. 
t 

4.  A  body  is  at  one  time  50' ft.,  and  at  another  75  ft., 
from  a  mass  of  rock;  what  are  the  relative   force^ 
exerted  upon  it  in  th'e  two  positions  ?          Ans.  9  :  4. 
^5.  Two  bodies,  one  weighing  6  Ibs.  and   the   other 
9  Ibs.,  are  attracting  a  third.     The  first  is  at  a  distance 
of  25  ft.,  the  second  of  oO  ft. ;  what  relative  attractions 
do  they  exert  ?  Ans.  24 . :  9. 

i-  6.  At  the  surface  of  the  earth  a  body  weighs  10  ft>s. ; 
what  would  it  weigh  if  carried  to  a  height  of  5  milea 
above  the  surface  ?  Ans.  9.97  Ibs. 

•  7.  A  glass  tube  1i=>inch  in  diameter  raises  water  by 
capillary  force  about  4  inches ;  how  high  will  water 
rise  in  a  tube  ^inch  diameter?  Ans.  -fa  in. 

8.  How  high  will  water  rise  between  two  parallel 
plates  -jigTJnch  apart  ?  Ans.  -f^  in. 

9.  If  Between  parallel  plates  -^  inch  apart,  water 
rises  two^ inches ;  how  high  will  it  rise  when  the  plates 
are  -fa  inch  apart  ?  Ans.  f-  in. 


NATURAL    PHILOSOPHY.  3$ 


CHAPTER   II. 


OF  THE  THREE  PHYSICAL  FORMS  OF  MATTER 
INTRODUCTION. 

APPLICATION   OF   THE  FUNDAMENTAL   IDEAS. 

(7.)  READ  (4).  Attraction  and  repulsion  acting  upon 
the  molecules  of  bodies,  produce  the  three  physical  forma 
of  matter:  solid,  liquid,  and  gaseous. 

Between  the  molecules  of  every  body,  two  sets  of 
forces,  attraction  and  repulsion,  are  continually  strug- 
gling. Just  in  proportion  as  one  or  the  other  prevails, 
the  body  will  be  a  solid,  a  liquid,  or  a  gas.  In  a  solid 
body  attraction  prevails,  and  its  molecules  are  firmly 
bound  together.  In  a  liquid  body  the  attraction  is 
almost  equaled  by  the  repulsion,  and  the  molecules  are 
left  free  to  move  easily  among  themselves.  In  a  gas- 
eous body  the  repulsion  exceeds  the  attraction,  and 
the  molecules  are  driven  away  from  each  other  to  the 
greatest  possible  distance.  The  solid  rock,  the  mobile 
water,  and  the  rushing  air,  are  types  of  these  three 
grand  divisions  to  which  all  bodies  belong. 

The  attraction  and  repulsion  among  the  molecules  of 
bodies  are  called  molecular  forces.      Cohesion,  adhe- 
sion, and  capillary  force  are  molecular  attractions ;  the 
force  of  heat  is  a  molecular  repulsion. 
2* 


34  NATURAL    PHILOSOPHY. 

Numerous  and  familiar  changes  of  form  are  due  to 
the  action  of  heat.  Ice,  for  example,  when  heated,  be- 
comes water,  and  water,  when  heated  still  more,  rises  in 
vapor  to  form  the  floating  clouds.  Or  suppose  the 
action  to  be  reversed.  Imparting  their  heat  to  other 
bodies,  the  clouds  are  changed  to  water,  and  water 
again  to  solid  ice  and  feathery  snow. 

Imitating  nature,  we  may  to  a  limited  extent,  by  the 
use  of  heat,  change  the  form  of  various  bodies,  and  nu- 
merous arts  of  life  spring  from  the  application  of  this 
power.  By  the  repulsive  force  of  heat  the  metallic 
ores  are  melted,  and  the  useful  metals  obtained.  By 
the  same  force  iron  is  liquefied,  that  it  may  be  molded 
into  requisite  forms  of  strength,  of  beauty,  or  of  use, 
demanded  in  the  arts.  The  expansive  force  of  steam  is 
but  the  repulsive  force  of  heat. 

§    1.    OF   THE    CHARACTERISTIC    PROPERTIES    OF    SOLID 
BODIES. 

(8.)  The  characteristic  properties  of  solid  bodies  are 
hardness,  tenacity,  malleability,  ductility,  and  crystal- 
line form. 

1.  Hardness. — The  particles  of  solid  bodies  are  held 
together  by  cohesion,  much  more  firmly  in  some  than  in 
others.  Those  in  which  they  are  held  with  the  greatest 
force,  will  most  successfully  resist  the  pressure  of  others. 
By  the  term  hardness,  we  refer  to  that  property  of  solids 
which  enables  them  to  resist  any  action  which  tends  to 
wear  or  scratch  their  particles  away. 

Hardness  does  not  imply  strength.  A  piece  of  glass 
will  scratch  an  iron  hammer,  which  proves  it  to  be 
harder  than  iron,  yet  glass  is  very  fragile,  easily  broken 


NATURAL    PHILOSOPHY.  35 

by  the  stroke  of  soft  wood ;  indeed,  by  almost  any  thing 
that  can  inflict  a  blow. 

Neither  does  hardness  imply  density.  The  diamond 
is  the  hardest  of  substances,  while  gold  is  so  soft  as  to 
be  easily  cut  with  a  knife ;  yet  gold  is  four  times  as 
dense  as  the  diamond.  Mercury  is  a  fluid,  and,  of 
course,  has  no  hardness,  yet  it  is  nearly  twice  as  dense 
as  the  hardest  steel. 

The  process  called  tempering  or  annealing,  consists  in 
regulating  the  hardness  of  a  body  by  the  action  of  heat. 
Steel,  when  in  its  hardest  condition,  is  too  brittle  .to  be 
used  in  the  arts ;  but  by  heating  it  to  a  temperature 
determined  by  the  use  to  be  made  of  it,  and  then  slowly 
cooling  it,  the  steel  may  receive  any  degree  of  hardness 
desirable.  It  may  be  made  almost  as  soft  as  soft  iron, 
or  it  may  become  nearly  as  hard  as  the  diamond . 

2.  Tenacity. — When  a  rod  of  iron  is  stretched  in  the 
direction  of  its  length,  it  will  be  found  that  great  force 
is  required  to  pull  it  apart.  The  property,  in  virtue  of 
which  bodies  resist  a  force  acting  in  the  direction  of 
their  length,  is  called  tenacity. 

The  metals  are  more  tenacious  than  other  solids,  and 
among  metals,  iron  in  the  form  of  cast-steel,  stands  at 
•the  head  of  the  list.  A  rod  of  cast-steel,  the  end  of 
which  has  an  area  of  one  square  inch,  will  support  a 
weight  of  134,256  pounds. 

It  has  been  found  by  experiment  that  the  tenacity 
.fa  bar  is  in  proportion  to  the  area  of  its  cross  section, 
*nd  entirely  independent  of  its  length. 

It  has  also  been  shown  that  the  tenacity  of  a  metal 
is  greatly  increased  by  drawing  it  into  wire.  The  cables 
of  suspension  bridges  are,  for  this  reason,  made  of  fine 
iron  "wire  twisted  together. 


36  NATURAL    PHILOSOPHY. 

3.  Malleability. — The  particles  of  many  solid  bodies 
may  be  displaced  without  overcoming  their  cohesion. 
By  the  blows  of  a  hammer,  the  molecules  of  many  metala 
may  be  shifted  about,  without  breaking  them  apart, 
until  the  bodies  are  reduced  to  the  form  of  thin  plates 
or  leaves.     By  passing  the  metal  between  the  rollers  of 
a  rolling-mill,  the  great  pressure  exerted  will  produce 
the  same  effect.     This  property,  in  virtue  of  which  a 
body  may  be  hammered  or  rolled  out  into  thin  leaves  or 
plates,  is  called  malleability. 

This  property  is  possessed  in  a  high  degree  by  many 
of  the  metals.  Under  the  hammer,  lead  is  the  most 
malleable  of  the  useful  metals ;  tin  stands  second,  and 
gold  third  on  the  list.  In  the  rolling-mill,  gold  is  the 
most  malleable,  silver  is  second,  copper  third,  while  tin 
stands  in  the  fourth  place  on  the  list.  (Cooke's  Chem- 
ical Physics,  p.  207.) 

4.  Ductility. — If,  instead  of  being  reduced  to  thin 
plates,  the  substance  may  be  drawn  into  wire,  the  prop- 
erty thus  shown  is  called  ductility.     This  property  is 
closely  allied  to  malleability,  but  metals  do  not  possess 
both  in  an  equal  degree.    Platinum,  for  example,  which 
is  seventh  on  the  list  of  malleable  metals,  stands  first 
on  the  list  of  those  which  are  ductile.     This  metal  has 
been  drawn  into  wire  finer  than  a  spider's  thread. 

5.  Crystalline  Form. — The    attraction   among   the 
molecules  has  not  brought  them  together  at  random, 
nor  in  disorder.     A  flake  of  snow,  when  seen  through 
a  microscope,  is  found  to  be  as  symmetrically  formed 
as  a  swan's  feather ;  ai^d  water  frozen  on  the  window 
panes  in  winter  shows  a  beautiful  variety  of  tree-like 
forms.    These  definite  and  regular  forms  in  which  solid 
substances  occur  are  called  crystals,  and  any  process  by 


NATURAL    PHILOSOPHY.  37 

which  they  may  be  obtained  is  called  a  process  of 
crystallization. 

In  the  formation  of  solid  bodies  their  tendency  to 
take  a  crystalline  form  is  almost  universal.  The  same 
substance  generally  takes  the  same  form,  but  in  differ- 
ent substances  the  shape  of  crystals  may  be  wonderfully 
unlike.  Lead,  in  its  most  common  ore,  called  galena, 
is  found  crystallized  in  cubes.  Specimens  of  these  cubes 
are  often  found  as  perfect  as  could  be  chiseled  by  an 
artist. 

But  the  larger  number-  of  solid  bodies  around  us  do 
not  appear  to  have  these  definite  crystalline  forms. 
They  have  been  made  solid  under  circumstances  which 
did  not  allow  the  molecular  forces  to  act  freely.  In 
many  cases,  however,  if  we  break  open  a  body  whose 
external  form  is  not  regular,  we  may  discover  that  it  is, 
after  all,  a  crystallized  body,  by  noticing  that  it  is  made 
up  of  multitudes  of  small  crystals,  very  closely  packed 
together.  This  is  true  of  many  rocks. 

Even  when  no  indication  of  a  crystalline  structure 
can  be  seen,  the  substance  can  often  be  made  to  assume 
it  by  some  artificial  process.  The  best  method  is  to 
dissolve  the  solid  in  water  or  some  other  liquid,  and 
allow  the  solution  to  stand  in  a  quiet  place  where  it 
may  evaporate  slowly.  Common  salt  and  alum  are 
substances  which  readily  and  beautifully  illustrate  this 
process.  The  more  slowly  the  water  evaporates,  the 
more  perfect  will  the  crystals  be.  (See  Cooke's  Chemi- 
cal Physics,  pp.  119  to  185.) 

§  2.  OF  THE  CHARACTERISTIC  PROPERTIES  OF  LIQUID  BODIES. 

(9.)  Liquids  have  elasticity  and  some  other  proper- 
ties in  common  with  solid  bodies.  But  since  the  attrao 


38  NATURAL    PHILOSOPHY 

tion  and  repulsion  among  their  molecules  are  very 
nearly  equal,  we  find  that  mobility  is  their  character 
istic  property. 

1.  Elasticity. — When  submitted  to  pressure  liquids 
are  compressed,  and  when  the  pressure  is  removed  they 
instantly  spring  back  to  their  original  volume.     It  re 
quires  a  very  great  force,  however,  to  compress  a  liquid 
in  the  least  degree  ;  so  great,  that  until  improved  means 
of  experiment  were  contrived,  liquids  were  thought  to 
l>e  incompressible.     Water,  at  a  freezing  temperature, 
when  pressed  by  a  force  of  15  Ibs.  to  the  square  inch, 
is  condensed  only  .0000503  of  its  volume.  (See  Ccoke's 
Chemical  Physics,  pp.  215  to  218.) 

The  force  with  which  a  liquid  springs  back  to  its 
former  size  after  being  compressed,  is  exactly  equal  to 
the  force  which  compressed  it ;  it  is,  for  this  reason, 
said  to  be  perfectly  elastic. 

2.  Attraction  and  repulsion  nearly  equal. — That  the 
attractive  and  repulsive  forces  among  the  molecules  of 
a  liquid  are  not  exactly  equal  may  be  shown  by  a 
pretty  experiment. 

To  one  end  of  a  scale-beam  (Fig.  3)  a  disk  of  brass  is 

suspended,  and  accurate- 
ly balanced  by  weights  in 
the  opposite  scale  pan. 
Now  let  the  disk  be 
brought  to  rest  upon  the 
surface  of  water  in  a  ves- 
sel, and  it  will  be  held 
=E-  there  with  considerable 

force.     If  the  disk  be  two  inches  in  diameter,  weights 
equal  to  200  grs.  may  be  piled  upon  the  opposite  pan 


NATURAL    PHILOSOPHY.  39 

before  it  will  be  torn  from  the  water.  Now,  notice 
that  a  film  of  water  still  adheres  to  the  disk,  having 
been  torn  away  from  the  water  beneath  it.  The  200 
grains  weight  have  simply  overcome  the  cohesion  of  the 
water.  We  thus  learn  that  the  attraction  is  a  trifle 
stronger  than  the  repulsion. 

But  the  attractive  and  repulsive  forces  are  nearly 
balanced,  and  if  we  now  remember  that  water  consists 
of  molecules,  it  is  not  more  difficult  to  see  that  there 
must  be  freedom  of  motion  among  them,  than  it  is  to 
see  that  a  number  of  smooth  balls  will  roll  easily  upon 
each  other. 

3.  Mobility. — To  illustrate  the  mobility  of  water, 
and  its  cause,  let  the  following  simple  experiment  be 
tried. 

Take  three  glass  goblets :  fill  one  with  small  marbles, 
one  with  fine  shot,  and  the  third  with  water.  After 
putting  a  dinner-plate  over  each  goblet,  they  may  be 
inverted  without  spilling  their  contents.  Now,  lift 
the  first,  and  the  marbles  will  roll  out  upon  the  plate. 
Lift  the  second,  and  the  shot  roll  out  in  the  same  way. 
A  person  at  a  distance  will  not  be  able  to  see  the 
separate  shot,  but  will  see  their  motion,  and  know  it  to 
be  caused  in  exactly  the  same  way  as  the  motion  of 
the  marbles,  which  could  be  seen  distinctly.  Now 
lift  the  third  goblet,  and  the  water  spreads  out  upon 
the  plate  exactly  as  did  the  marbles  and  the  shot.  The 
molecules  of  water  are  balls  infinitely  smaller  than 
shot ;  but,  while  the  most  powerful  microscope  fails  to 
reveal  them,  the  mind  can  see  them,  so  small,  so  round 
and  smooth,  that  they  roll  and  glide  among  themselves 
with  the  greatest  freedom. 

The  phenomena  peculiar  to  liquid  bodies   depend 


40  NATURAL    PHILOSOPHY. 

chiefly  upon  the  mobility  of  their  particles.  The 
phenomena  of  liquids  at  rest  must  be  now  considered  : 
those  of  liquids  in  motion  must  be  reserved  for  a  future 
chapter. 


§  3.   OF   LIQUIDS   AT  BEST. 

(10.)  At  any  point  inside  of  a  body  of  liquid  there 
is  equal  pressure  from  all  directions. 

Hence  a  fluid  will  rest  only  when  its  upper  surface 
is  level.  And  the  level  surface  of  a  large  body  of 
water  is  convex. 

1.  Liquids  press  in  all  directions. — In  order  to  see 
that,  because  the  particles  of  a  liquid  are  free  to  move, 
they  must  be  exerting  pressure  in  all  directions,  we 
will  suppose  a  number  of  very  smooth  balls  to  be 
arranged  as  in  Fig.  4.  The  weight  of 
the  ball  A  will  be  a  downward  press- 
ure upon  the  balls  B  and  C.  These, 
being  free  to  move,  will  be  pushed 
aside.  The  ball  B,  moving  toward 
the  left,  will  push  between  the  balls  D  and  E,  while 
the  ball  E,  moving  upward,  will  exert  an  upward 
pressure. 

Just  so  the  small  molecules  of  a  liquid  are  exerting 
pressure  downward,  upward,  and  laterally;  and,  more- 
over, if  the  liquid  be  at  rest,  every  point  in  it  must  be 
pressed  equally  in  all  these  directions. 

An  experiment  may  help  to  illustrate  this  principle. 
If  a  disk  of  metal  be  held  in  the  middle  of  a  jar  of 
water,  it  is  easy  to  see  that  it  must  be  pressed  down- 
ward by  the  weight  of  the  water  just  above  it ;  but  it 


NATURAL    PHILOSOPHY.  4] 

may  not  be  so  clear  that  it  is  pushed  up  by  an  equal 
force.  Taking  a  lamp  chimney,  and  put-  Fis- 5 
ting  the  string  handle  of  the  disk  C,  Fig.  5, 
through  it,  hold  the  disk  tightly  against  the 
lower  end  of  the  tube  until  it  is  pushed 
down  to  the  middle  of  the  water.  Now  jj 
loosen  the  string :  the  heavy  disk  does  not 
sink,  but  remains  tightly  pressed  upvmrd 
against  the  tube  by  the  water.  If  water  be 
allowed  to  enter  the  tube  it  will  press  down 
upon  the  disk,  and  when  it  has  filled  the  tube  almost 
to  a  level  with  the  water  outside,  then  the  disk  falls, 
suggesting  that  the  upward  and  downward  pressures 
are  equal. 

Numerous  simple  experiments  might  be  given  to 
illustrate  this  important  principle :  one  other  must 
suffice.  Glass  is  eminently  brittle.  It  may  be  blown 
into  sheets  as  thin  as  the  finest  paper  cambric.  In  this 
condition,  the  weight  of  a  few  grains  resting  upon  it 
in  the  air  would  crush  it.  Yet,  placed  near  the  bottom 
of  the  deepest  cistern,  it  will  support  the  weight  of  all 
the  water  above  it,  and  remain  unbroken.  This  could 
not  happen,  if  the  pressure  of  the  water  upon  it  was 
not  equal  from  all  directions. 

2.  TJie  surface  of  water  at  rest  is  level. — The  truth 
of  this  principle  may  be  seen  by  attentively  examining 
Fig.  6,  which  represents  a  section  of  a  vessel  contain- 
ing water,  the  surface  of  which  has  for  the  moment 
been  thrown  into  the  position  indicated  by  the  line 
A.  E.  Refer  to  any  two  points  in  the  water,  as  h  and  K 
We  see  that  the  downward  pressure  at  A,  would  be  the 
weight  of  the  water  above  that  point — a  column  m  h. 
But  the  pressure  at  that  point  is  equal  in  all  directni  o. 


42  NATURAL    PHILOSOPHY. 


p  so  that  the  water  be 
tween  h  and  K  would 

^    be  pressed  toward  K  by  a 

E  force  equal  to  the  weight 
of  the  column  ra  A.  In 
just  the  same  way  we  may 

c*  show  that  at  K,  the  water 
is  being  pressed  toward  A  by  a  force  equal  to  the  weight 
of  the  column  n  K.  The  column  m  A  is  greater 
than  n  K,  and  since  the  water  is  free  to  move  it  will 
yield  to  the  greater  pressure,  and  go  toward  K  until 
the  two  forces  are  equal.  The  two  forces  will  be  equal 
only  when  m  and  n  are  in  the  same  level  surface,  a  b. 

3.  But  a  level  surface  is  convex. — The  surface  of 
water  will  be  at  rest  when  the  force  of  gravitation  acts 
upon  all  points  of  it  alike.  That  the  attraction  of  the 
earth  may  be  equal  on  all  points,  they  must  be  equally 
distant  from  the  center  of  the  earth.  To  be  at  the 
same  distance  from  the  center  of  the  earth  they  must 
form  a  curved  surface.  In  case  of  large  bodies  of 
water,  of  the  oceans  for  example,  the  convexity  can 
be  seen.  It  is  shown  by  the  ancient  observation  that 
the  topmast  of  an  approaching  ship  is  the  part  first 
Been  from  port. 

(11.)  Since  the  surface  of  water  at  rest  must  be  level, 
we  infer  that  water  confined  in  pipes  or  close  channels 
will  always  rise  as  high  as  the  source  from  which  it 
comes. 

Upon  this  principle  cities  are  often  supplied  with  watei . 

The  same  principle  explains  the  phenomena  of 
springs  and  artesian  wells. 

1.    Water  in  pipes  will  rise  as  high  as  its  source. — 


NATURAL    PHILOSOPHY.  43 

If  into  one  arm  of  a  bent  tube  we  ponr  water,  it  wil? 
flow  around  into  the  other,  until  it  stands  at  the  same 
height  in  both.  No  matter  what  may  be  the  shape  of 
the  vessel,  the  surface  of  the  liquid  it  holds  must  be 
just  as  high  in  one  part  of  it  as  in  another,  and  a  pipe 
leading  from  a  vessel  is  a  part  of  the  vessel  which  holds 
the  water. 

2.  The  supply  of  water  to  cities. — A  pipe  leading 
from  a  reservoir  of  water  on  a  hill  outside  a  city,  may 
be  buried  in  the  ground,  passed  down  the  hill-side,  and 
through  the  streets,  and  be  provided  with  branches  lead- 
ing into   cisterns   in    every  dwelling.      Unless   these 
cisterns  are  higher  than  the  water  in  the  distant  reser- 
voir, the  water  will  flow  down  the  hill-side,  through 
the  streets  and  up  the  branches  into   the  dwellings, 
and  supply  them  all  with  water.     Many  cities  are,  in 
this  way,  conveniently  supplied  with  abundance   of 
water,  for  private  dwellings  not  only  but  for  public 
fountains  and  manufacturing  purposes. 

3.  Springs. — The  rocks  which  compose  the  earth  are 
arranged  in  layers,  called  strata,  which  are  generally 
more  or  less  oblique  as  represented  in  Fig.  7.     Some 
of  these  strata  will  allow  water  to  soak  through  them ; 
others  will  not.     In  the  figure  the  dotted  portions  a  a  a 
indicate  the  porous  strata.  , 

Now,  water  falling  on  the  surface  of  the  earth  at  0, 
will  settle  through  the  loose  or  porous  material  until 
it  reaches  the  rock,  which  it  can  not  penetrate.  Flow- 
ing along  the  surface  of  this  rock,  it  will  issue  from  the 
hill-side  at  S,  and  thus  form  a  spring. 

4.  Artesian  wells. — Again,  the  water,  falling  upon 
the  surface  and  passing  through  other  porous  layers, 
comes  in  contact  with  a  rock  which  it  can  not  penetrate. 


44  NATURAL    PHILOSOPHY. 

and  flows  along  its  surface.   The  basin-shaped  part,  a  0, 
of  the  porous  layer,  would  thus  in  time  become  filled 


Fig.  7. 


with  water ;  indeed  the  entire  layer  reaching  to  the  sur- 
face of  the  earth  in  both  directions  might  thus  be  filled. 
If,  then,  a  well  at  W  be  sunk  through  the  mass  down  to 
this  saturated  layer,  the  water  will  rise  in  the  well, 
sometimes  to  the  surface  of  the  ground  above,  and 
often  spout  in  jets  many  feet  above  it. 

Such  wells  are  often  bored  to  very  great  depths  and 
are  called  artesian  wells.  One  of  these  wells  was  bored 
in  Louisville,  Kentucky,  to  the  depth  of  2,086  feet.  An 
other  in  St.  Louis  has  a  depth  of  2,199  feet.  The  supply 
of  water  furnished  is  often  very  abundant.  The  famous 
Grenelle  well,  in  Paris,  yields  daily  600,000  gallons. 

(12.)  The  pressure  of  a  liquid  on  the  bottom  of  tho 
vessel  which  holds  it  is  independent  of  the  shape  of  tho 
vessel.  It  depends  on  the  depth  of  the  liquid,  and 
equals  the  weight  of  a  column  whose  base  is  tho 


NATURAL    PHILOSOPHY, 


45 


Fig.  8. 


of  the  vessel,  and  whose  height  is  the  depth  of  the 
liquid  in  it. 

1.  The  pressure  is  independent  of  the  shape  of  tfo 
wssel. — This  may  be  proved  by  experiment.      The 
•s^ential  parts  of  an  apparatus  for  this  purpose  are  re- 
pr.ssented  in  Fig.  8.     A  glass  tube,  A  B,  bent  twice 
nt  right  angles,  con- 

Vaias  mercury.  The 
height  of  the  mercury 
in  one  arm  is  shown 
by  n  graduated  scale, 
and  to  the  other  arm 
vessels  of  various 
forms  and  heights 
may  be  attached. 
When  a  vessel,  Gr, 
is  filled  with  water,  the  fluid  presses  upon  the  mer- 
cury at  A,  and  pushes  it  up  in  the  arm  C  D  ;  the 
height  to  which  it  rises  being  shown  by  the  gradu- 
ated scale.  Now  let  the  vessel  be  removed,  and 
another,  in  the  form  shown  at  E,  be  put  in  its  place. 
If  water  be  poured  into  this  vessel  until  it  stands  as 
high  as  it  did  in  the  other,  the  mercury  will  be 
seen  to  rise  in  CD  to  the  same  point  as  before. 
Vessels  of  various  other  forms  may  be  used,  but  if  all 
are  of  the  same  height  the  water  which  fills  them  will 
push  the  mercury  to  the  same  point  on  the  scale.  We 
infer  that  the  pressure  of  a  fluid  downward  is  quite  in- 
dependent of  the  shape  of  the  vessel  and  the  quantity 
of  fluid. 

2.  The  pressure  depends  on  the  depth  of  the  liquid.  — 
If  a  tube  twice  as  high  as  the  vessel  E,  in  Fig.  8,  be 


46  NATURAL    PHILOSOPHY. 

•used  and  filled  with  water,  the  mercury  will  be  seea  to 
rise  just  twice  as  far  as  when  the  other  vessels  were 
employed,  and  by  repeated  experiment  it  is  seen  that 
the  pressure  is  in  proportion  to  the  height  ot  the 
column  of  water  which  exerts  it.  (See  Cooke's  Chem- 
ical Physics,  p.  223). 

\,  3.  To  calculate  the  pressure. — If  the  pressure  de* 
pends  only  on  the  size  of  the  base  and  the  height  of  the 
column,  then  it  must  equal  the  weight  of  a  column 
whose  base  is  the  base  of  the  vessel,  and  whose  height 
is  the  depth  of  the  liquid.  Now,  one  cubic  foot  of  water 
weighs  62£lbs.,  and  if  the  number  of  cubic  feet  of 
water  which  exerts  the  pressure  be  multiplied  by  62|, 
the  amount  of  pressure  in  pounds  will  be  obtained. 
Thus,  suppose  a  vessel,  represented  by  E  F  C  D,  in 

Fig.  9,  to  be  full  of  water : 
the  pressure  on  its  bottom 
is  the  weight  of  the  column 
A  B  C  D.  Let  the  area  of 
the  bottom  be  3  square  feet, 
and  the  depth  of  the  water  be 
8  feet ;  then  24  cubic  feet  of 
water  exerts  the  pressure,  and  24:  x  62J  Ibs.,  or  1,500  Ibs. 
is  the  pressure  exerted. 

Now,  since  the  pressure  is  equal  in  all  directions,  we 
may  obtain  the  amount  of  pressure  against  any  portioi 
of  surface  either  in  the  bottom  or  sides  of  the  vessel 
by  getting  the  weight  of  a  column  of  water  whose  bast 
is  the  surface  pressed  upon,  and  whose  height  is  the 
depth  of  the  water  to  the  middle  point  of  that  surface. 
For  example,  suppose  we  would  know  how  much  press- 
ure is  borne  by  one  square  foot  of  the  side  of  a  vessel 
at  a  depth  of  ten  feet  below  the  surface  of  the  water. 


NATURAL    PHILOSOPHY. 


47 


We  must  understand  that  ten  feet  is  the  distance  from 
the  top  of  the  water  to  the  middle  point  of  the  square 
foot ;  then  the  pressure  will  be  the  weight  of  a  column 
of  water  whose  base  is  one  square  foot  and  whose  height 
is  ten  feet.  Sfcich  a  column  will  contain  10  cub.  ft.  of 
water,  and  its  weight  will  be  10  x  62  J  Ibs. 

t>  >  .*  v 

v  (13.)  A  solid  body  when  immersed  m  a  fluid,  is 
pushed  upward  by  it  with  a  force  equal  to  the  weight 
of  the  fluid  it  displaces. 

It  follows  from  this  principle,  1st.  That  a  solid  body, 
lighter  than  water,  will  sink  far  enough  to  displace 
water  whose  weight  is  equal  to  its  own.  2d.  That  a 
solid  body,  heavier  than  water,  will  weigh  less  in  water 
than  in  air,  the  difference  being  the  weight  of  the  watei 
displaced  by  it. 

1.  Solid  bodies  in  water  are  pressed  upward. — If,  foi 
example,  a  piece  of  wood  be  pushed  down  into  a  vessei 
of  water  we  find  it  struggling  to  rise  to  the  surface.     It 
Is  pressed  upward  by  the  water  under  it,  and  consider- 
able force  of  the  hand  is  required  to  keep  it  down.     Or 
if  a  stone  be  suspended  in  water  it  feels  lighter  than 
when  in  air ;  the  water  under  it  pushes 

upward  against  it,  and  thus  supports  a 
part  of  its  weight. 

2.  With  force  equal  to  the  weight 
of  water    displaced. — Now,    suppose 
a  block   of   marble   suspended   in    a 
vessel  of  water  (Fig  10).      The   up- 
ward pressure  against  its  lower  surface, 
a  &,  is  equal  to  the  downward  pressure 
of  the  water  at  that  depth,  and  this 
downward    pressure    is  equal  to   the 


Fur.  10. 


1%  NATURAL    PHILOSOPHY. 

weight  of  the  column  of  water,  efl  a.  Now  the  column 
of  water,  efcd,  is  sustained  by  a  part  of  this  upward 
pressure,  and  the  rest  of  it  is  exerted  upon  the  marble. 
To  sustain  the  column,  efc  d,  requires  an  upward  press- 
ure equal  to  its  weight,  and  hence  therefcs  left  a  press- 
ure against  the  surface,  a  &,  equal  to  the  weight  of  a 
column  of  water,  a  b  c  d,  but  this  water  is  displaced  by 
the  marble.  The  upward  pressure  against  the  block 
is,  therefore,  equal  to  the  weight  of  the  fluid  displaced. 

We  owe  the  discovery  of  this  important  principle  to 
Archimedes,  one  of  the  most  eminent  philosophers  of 
antiquity,  and  to  this  day  it  is  called  the  principle  of 
Archimedes.  Its  applications  are  numerous.  It  helps 
the  chemist  to  distinguish  one  substance  from  another, 
and  the  merchant,  often,  to  judge  of  the  purity  and 
value  of  his  merchandise.  In  any  case  it  enables  the 
inquirer  to  determine  the  size  or  volume  of  a  solid 
body,  however  irregular,  and  it  has,  moreover,  led  to 
valuable  improvements  in  marine  architecture  and  in 
other  arts. 

3.  If  the  solid  is  lighter  than  water. — The  weight 
of  the  water  displaced  by  a  block  of  wood  will  just 
equal  the  weight  of  the  wood  itself.  A  pound  of  wood 
will  displace  a  pound  of  water,  but  a  pound  of  wood  is 
larger  than  a  pound  of  water,  so  that  only  part  of  the-, 
wood  will  be  immersed.  A  tin  basin  and  a  wooden 
bowl  of  the  same  size,  will  displace  an  equal  volume  of 
water,  if  the  walls  of  the  basin  are  thin  enough,  so  that 
the  two  bodies  have  the  same  weight.  Upon  this  prin 
ciple  iron  ships  are  built.  An  iron  ship  will  sink  no 
farther  than  one  of  wood  of  the  same  size,  provided  the 
walls  of  iron  are  BO  thin  that  the  two  ships  shall  be  of 
the  same  weight. 


NATURAL    PHILOSOPHY.  4.9 

4.  If  the,  solid  is  heavier  than  water. — If  a  solid 
be  heavier  than  water,  the  upward  pressure  of  the 
fluid  can  support  only  a  part  of  its  weight.  The  weight 
supported  will  be  the  weight  of  the  water  which  the 
Bolid  displaces*  Thus,  for  example,  a  piece  of  marble 
which  weighs  10  ozs.  in  air,  will  be  found  to  weigh  only 
6.3ozs.  in  water.  The  upward  pressure  of  the  water 
is  equal  to  3.7  ozs.,  and  this  is  the  weight  of  the  water 
which  the  marble  displaces,  and  whose  bulk  is,  of 
course,  just  equal  to  the  bulk  of  the  marble: 

(14.)  The  specific  gravity  of  a  substance  is  its  weight 
compared  to  the  weight  of  an  equal  bulk  of  some  other 
body  taken  as  a  standard. 

To  obtain  it,  different  methods  must  be  taken,  accord- 
ing as  the  body  is  a  gas,  a  liquid  or  a  solid. 

1.  Specific  Gravity. — The  specific  gravity  of  a  sub- 
stance shows  how  many  times  heavier  it  is  than  an 
equal  bulk  of  some  other  body.  The  standards  used  are 
water  and  air  ;  water  for  all  solid  and  liquid  bodies,  and 
air  for  all  gases.  Then,  when  we  say,  for  instance, 
that  the  specific  gravity  of  gold  is  19,  we  only  mean 
that  a  cubic  inch  of  gold  will  weigh  19  times  as  much 
as  a  cubic  inch  of  water.  The  specific  gravity  of 
oxygen  gas  is  1.106  :  that  is  to  say,  a  cubic  inch  of 
oxygen  gas  will  weigh  1.106  as  much  as  a  cubic  inch 
of  air.  The  following  simple  rule  must  evidently  cover 
all  cases  of  getting  specific  gravity : — Divide  the  weight 
of  the  body  by  the  weight  of  an  equal  'bulk  of  the  stand- 
ard. 

/ 

L OF   GASES. 

A. — To  obtain  the  specific  gravity  of  a  .gas,  divide 

2 


50  NATURAL    PHILOSOPHY. 

the  weight  of  a  convenient  portion  of  it  by  the  weight 
of  an  equal  portion  of  air. 

To  get  the  weight  of  equal  portions  of  gases  is,  how- 
ever, a  difficult  process,  requiring  many  precautions. 
"Without  trying  to  give  the  details  of  the  operation 
(see  Cooke's  Chem.  Phys.,  pp.  93  and  667),  we  may  de- 
scribe it  in  general  terms.  A  glass  globe  is  first 
weighed  when  full  of  air.  The  air  is  then  taken 
out  of  it  by  means  of  an  air-pump,  and  the  globe  is 
again  weighed :  the  difference  in  these  weights  is  the 
weight  of  the  globe  full  of  air.  The  globe  is  then  filled 
with  the  gas  whose  specific  gravity  is  desired,  and 
again  weighed :  the  difference  between  this  weight  and 
that  of  the  empty  globe,  is  the  weight  of  the  globe  fall 
of  gas.  The  specific  gravity  is  obtained  from  these 
weights  of  equal  volumes  of  gas  and  air. 


^n. — OF  LIQUIDS. 

B. — The  specific  gravity  of  a  liquid  may  be  obtained 
in  various  ways.  We  may  notice — 

1.  By  direct  weighing. 

2.  By  an  instrument  called  the  hydrometer. 

3.  By  the  use  of  a  solid  bulb. 

1.  By  direct  weighing. — The  most  direct  method  of 
getting  the  specific  gravity  of  a  liquid,  is  to  weigh 
equal  quantities  of  it  and  water,  and  then  divide  the 
weight  of  the  liquid  by  that  of  the  water.  To  facilitate 
the  operation,  "  specific  gravity  bottles "  are  made, 
which  hold  just  1,000  grains  of  pure  water.  The  weight 
of  the  bottle  being  known,  a  single  operation  with  the 


NATURAL    PHILOSOPHY. 


balance  will  give  the  weight  of  the  liquid,  and  then  its 
specific  gravity  may  be  speedily  calculated. 

2.  By  the  hydrometer. — A  common  form  of  this  instru- 
ment is  represented  in  Fig.  11.     It  consists  of  a  glasa 
tube,  with  two  bulbs  near  its  lower  end.  The      rig.  11. 
tube  and  upper  bulb  are  full  of  air,  which 
renders  the  instrument  lighter  than    water. 
The  lower  and  smaller  bulb  contains  shot 
enough  to  keep  the  instrument  in  an  erect 
position,  when  placed  in  a  liquid,  as  shown 
in  the  figure.     A  graduated  scale  is  fixed  to 
the  stem,  to  indicate  the  depth  to  which  the 
instrument  sinks  in  different  liquids. 

The  action  of  this  instrument  can  be  read- 
ily, explained  by  means  of  a  piece  of  wood, 
several  inches  long  and  an  inch  square,  hav- 
ing its  lower  end  loaded  with  wire.  If  this 
be  put  into  a  vessel  of  water,  it  will  sink  to  a  certain 
depth,  and  remain  upright.  If  it  sinks  10  inches, 
then  10  cubic  inches  of  water  are  displaced  by  it.  If 
now  the  instrument  be  put  into  a  vessel  of  alcohol,  it 
will  sink  deeper,  suppose  it  be  12  inches ;  then  12  cubic 
inches  of  alcohol  are  displaced.  But,  according  to  the 
principle  of  Archimedes,  the  fluid  displaced  is  equal  in 
weight  to  the  body  floating  in  it  [see  (13),  1  and  2]. 
Hence  10  cubic  inches  of  water  have  the  same  weight 
as  12  cubic  inches  of  alcohol,  or  alcohol  is  -fj-  as  heavy 
as  water.  Its  specific  gravity  is,  therefore,  {%  =  833  +  . 

Making  the  instrument  of  glass,  and  giving  it  the 
form  seen  in  Fig.  11,  renders  it  more  convenient,  but 
does  not  alter  the  principle  on  which  it  acts. 

The  graduation  of  the  scale  is  arbitrary,  and  varies 
in  different  forms  of  the  instrument.  The  zero  usually 


52  NATURAL    PHILOSOPHY. 

marks  the  point  to  which  the  Irydrometer  sinks  in  pure 
water,  and  the  degrees  above  and  below  show  how  far 
the  instrument  may  sink  in  liquids  respectively  lighter 
and  heavier  than  water. 

3.  By  ike  use  of  a  lulb. — According  to  the  prin 
ciple  of  Archimedes,  a  heavy  bulb  of  glass,  or  other 
convenient  substance,  when  weighed  in  any  liquid,  will 
lose  a  part  of  its  weight  just  equal  to  the  weight  of  an 
equal  bulk  of  that  liquid.  Hence,  weigh  a  bulb  of  glass 
in  air,  afterward  in  water,  and  then  in  the  liquid  whose 
specific  gravity  is  desired.  The  losses  of  weight  it  sus- 
tains will  be  the  weights  of  equal  bulks  of  the  two 
liquids,  and  from  these  weights  the  specific  gravity  may 
be  obtained, 

To  illustrate  this  method,  suppose  the  specific  grav- 
ity of  alcohol  is  to  be  found.  A  bulb  of  glass,  weighed 
in  air  and  then  in  water,  is  found  to  lose  325  grs.  Ita 
loss  in  alcohol  is  found  to  be  257  grs.  Then  HJ=.79  + 
is  the  specific  gravity  of  the  alcohol.  ^ 

m. — OF  SOLIDS. 

0. — There  are  two  important  cases  of  common  oc« 
currence : — 

1.  The  solid  is  heavier  than  water. 

2.  The  solid  is  lighter  than  water. 

1.  Of  a  solid  heavier  than  water. — Divide  the  weight 
of  the  body  in  air,  by  its  loss  of  weight  in  water.  The 
principle  of  Archimedes  explains  this  rule. 

Thus  the  weight  of  marble  [see  (13),  4]  in  air  being 
lOozs.,  and  in  water  being  6.3ozs.,  it  is  clear  that  the 
difference,  3.7,  is  the  weight  of  a  bulk  of  water  equal 


NATURAL    PHILOSOPHY. 


B 


to  the  size  of  the  marble.     Then,  -j^-  =  2.7  is  the  speci- 
fic gravity  of  this  solid. 

The  experiment  is  conducted  in  the  following 
manner.  Let  the  specific  Fig.  12. 

gravity  of  iron  be  desired. 
A  fragment  of  iron  of  con- 
venient size  is  hung  from 
the  bottom  of  one  scale 
pan  of  a  balance,  and 
weighed.  It  is  then  im- 
mersed in  a  vessel  of 
water  (see  Fig.  12),  and 
its  weight  again  deter- 
mined. 

^N"ow5  suppose  the  iron  weighs,  in  air,  360  grs.,  and  in 
water,  313.85 grs.  Then  360  —  313.85  =  46.15  grs.  is 
the  weight  of  an  equal  bulk  of  water.  And  ^-fj  =7.8 
is  the  specific  gravity  of  the  iron. 

2.  Of  a  solid  lighter  than  water. — If  the  solid  be 
lighter  than  water,  the  operation  is  more  complex.  If 
the  light  body  be  compelled  to  sink  in  water  by  fasten- 
ing to  it  some  heavier  body,  their  loss  of  weight  will 
represent  the  upward  pressure  of  the  water  upon  them 
both.  If  the  heavy  body  alone  be  weighed  in  water, 
its  loss  will  represent  the  upward  pressure  against  it. 
Now,  if  the  upward  pressure  against  the  heavy  body 
be  subtracted  from  the  upward  pressure  upon  both,  the 
difference  must  represent  the  upward  pressure  against 
the  light  body  alone,  and  hence,  the  weight  of  a  quan- 
tity of  water  equal  to  its  bulk. 

To  illustrate  this  operation,  suppose  a  body  weighed, 
in  air,  200  grs.  When  attached  to  a  piece  of  lead, 
both  weighed  1,936  grs.  in  air,  and  1,460  grs.  in  water. 


NATURAL    PHILOSOPHY. 


Buffering  a  loss  of  476  grs.  The  lead  itself,  when 
veighed  in  water,  lost  152  grs.  The  upward  pressure 
against  the  light  body  alone  must  then  have  been, 
476  —  152  =  324  grs.  Then,  200  grs.,  the  weight  of 
the  light  body  in  air,  divided  by  324  grs.,  the  weight 
of  an  equal  bulk  of  water,  is  the  specific  gravity  desired. 
In  the  following  table  the  Specific  gravity  ^  various 
substances  are  arranged  for  reference,  j 

I. OF   GASES,   AT   32°  F.      BAROMETER,    30   INCHES. 


Names.  Sp.  gr. 

Air 1.000 

Oxygen 1.106 

Hydrogen 0.0691 


Names.  Sp.  gr. 

Nitrogen 0.972 

Carbonic  Acid 1.529 

Olefiant  Gas. .  .  .0.978 


II. OF  LIQUIDS,  AT  39°  F. 


Names. 
'Water  (distilled)  

Sp.  gr. 
1.000 

Names. 
•^Ether  

Sp.gr. 
0.715 

Sea  Water  

...    .1026 

^Naphtha  

0.847 

Milk  

1.030 

**  Oil  Turpentine  

...   0.869 

Alcohol  (absolute) 

...   0  792 

"Wine-  of  Burgundy 

0  991 

Olive  Oil  

....0.915 

•ix  Mercury  (32"  v.)  

..   13.596 

III.— OF  SOLIDS,  AT  39°  F. 


Names.  8p.  gr. 

Platinum 21.5 

•'Gold  (cast) 19.26 

^Iron       »     7.2 

Steel 7.8 

"Lead  (cast) 11.3 

•  Copper  "    .8.8 


Names.  Sp.  gr. 

^Silver  (cast) 10.47 

Diamond 3.50 

^Marble 2.70 

Ivory 1  92 

•'Ice 0.93 

wood 0.66 


4- 


(15.)  If  an  external  pressure  be  exerted  upon  any 
portion  of  the  surface  of  a  liquid,  the  same  amount  of 
pressure  will  be  transmitted  equally  in  every  direction. 


NATURAL    PHILOSOPHY.  55 

This  is  true,  whatever  may  be  the  form  of  the  vessel 
which  contains  the  liquid.  This  is  the  principle  ap- 
plied in  the  hydrostatic  press. 

1.  The  equal  transmission  of  pressure. — To   illus- 
trate the  principle  stated  above,  let  a  vessel,  repre- 
sented in  section  by  Fig.  13,  be  quite  filled  with  water. 
In  the  sides  of  the  vessel  are  several 

apertures,  A,  B,  C,  D,  and  E,  closed 
with  movable  pistons.  Let  the 
area  of  each  piston  be  1  sqr.  in., 
and  suppose  a  weight  of  two 
pounds  be  placed  upon  the  pis- 
ton A.  It  will  be  found  that  a 
force  of  two  pounds  will  be  ex- 
erted against  each  of  the  other 
pistons.  Thus  E  will  be  pushed  upward  by  a  force  of 
two  pounds,  while  B  and  D  will  at  the  same  time  be 
pushed  in  opposite  directions,  each  with  a  force  of  just 
two  pounds.  No  matter  how  numerous  these  pistons 
may  be,  nor  in  what  direction  they  may  be  inserted,  each 
will  be  found  exerting  a  two-pound  pressure  under  the 
influence  of  a  force  of  two  pounds  acting  at  A.  Every 
square  inch  in  the  entire  surface  of  the  vessel  will  re- 
ceive a  pressure  of  two  pounds. 

2.  The  shape  of  the  vessel  makes  no  difference.- 
The  vessel  may  be  of  any  shape  whatever,  and  an  equal 
pressure  will  be  received  on  every  square  inch  of  its 
surface  whenever  an  external  force  is  applied.     We 
will  suppose,  for  illustration,  that  the  vessel  is  a  bent 
tube  in  the  form  of  the  letter  U. 

A  pressure  may  be  exerted  upon  the  water  in  one 
arm,  by  forcing  the  breath  into  the  open  end  of  th« 


56  NATURAL    PHILOSOPHY. 

lube.  The  liquid  will  go  down  in  that  arm  and  rise  IE 
the  other.  The  pressure  of  the  breath  is  downward  in 
one  arm ;  it  is  lateral  through  the  bend,  and  upward 
in  the  other  arm.  Moreover,  these  pressures  are  all  ex- 
actly equal. 

But  suppose  one  arm  of  this  tube  to  be 
larger  than  the  other.  Let  the  vessel  have 
the  form  represented  in  Fig.  14,  the  arm  A 
being  twice  as  large  as  the  other.  To  push 
the  water  down  in  II  G,  requires  no  greater 
effort  with  the  breath  than  when  the  arms 
were  of  equal  size.  The  downward  press- 
ure on  one  square  inch  at  H,  is  transmitted 
as  an  equal  upward  pressure  on  each  square 
inch  at  A,  and  thus  a  column  twice  as 
large  is  lifted  one-half  as  high  by  tho 
_  same  force.  ^  t/ 
3.  The  hydrostatic  press. — The  hydrostatic  press 
acts  upon  the  principle  just  explained.  It  is  a  machine 
by  which  a  small  force  may  be  made  to  exert  a  great 
pressure.  Its  construction  may  be  understood  by  ex- 
amining Fig.  15. 

Two  metallic  cylinders,  A  and  B,  of  different  sizes, 
are  joined  together  by  a  tube  K.  In  the  small  cylinder 
there  is  a  piston,  p,  which  can  be  moved  up  and  down 
by  the  handle  M.  In  the  large  cylinder  there  is  also  a 
piston,  P,  having  at  its  upper  end  a  large  iron  plate 
which  moves  freely  up  and  down  in  a  strong  framework, 
Q.  Between  the  iron  plate  and  the  top  of  this  frame- 
work, the  body  to  be  pressed  is  placed. 

Now,  when  the  small  piston  is  raised,  the  cylinder  A 
Is  filled  with  water  drawn  from  the  reservoir  H,  below* 
and  when  it  is  pushed  down,  ihib  water  \&  forced  into 


NATURAL    PHILOSOPHY.  57 

the  large  cylinder,  through  the  pipe  K.  There  is  a 
valve  in  this  tube  which  prevents  the  water  from  re- 
turning, so  that  each  stroke  of  the  small  piston  pushes* 
an  additional  quantity  of  water  into  the  larger  cylinder. 
By  this  means  the  large  piston  is  pushed  up  against  the 
body  to  be  pressed. 

To  calculate  the  pressure  exerted  by  the  large  piston, 
we  must  remember  that  the  force  acting  upon  the  pis- 
Fig.  i& 


ton  in  A,  will  be  exerted  upon  every  equal  amount  ot 
surface  in  B.    To  illustrate  this  :  suppose  the  area  of  the 
large  piston  to  be  ten  times  the  area  of  the  small  one 
then  one  pound  at  A  will  produce  a  pressure  of  ten 
pounds  at  P.     The  handle,  M,  increases  the  advantage 

3* 


58  NATURAL    PHILOSOPHY. 

still  more,  according  to  the  principle  of  the  lever  to  be 
explained  in  a  future  chapter. 

By  increasing  the  size  of  the  large  cylinder,  and 
diminishing  the  size  of  the  small  one,  the  pressure 
exerted  by  a  given  power  will  be  increased  proportion- 
ally. The  weight  of  a  man's  hand  might  thus  be  made 
to  lift  a  ship  with  all  its  cargo.  The  only  limit  to  the 
increase  of  power  would  be  the  strength  of  the  material 
of  which  the  machine  is  made. 


PROBLEMS   ILLUSTRATING  THE   LAWS   OF   HYDROSTATICS. 

1.  A  cylindrical  vessel,  whose  base  is  5  sq.  ft.,  is  10  ft. 
high.    It  is  filled  with  water.  "What  pressure  is  exerted 
upon  the  base  ?  A  ns.  3,125  Ibs. 

2.  If  the  bottom  of  a  vessel  has  an  area  of  72  sq.  in., 
and  its  top  an  area  of  96  sq.  in.,  and  it  is  9  in.  high  ; 
what  pressure  will  be  exerted  on  the  bottom  when  the 
vessel  is  full  of  water  ?  Ans.  23.43  Ibs. 

3.  Two  vessels  with  equal  bases  are  filled  with  water, 
one  to  a  height  of  9  in.,  the  other  to  a  height  of  27  in. 
How  many  times  more  pressure  on  the  base  in  the  last 
case  than  in  the  first  ?  Ans.  3. 

4.  How  much  pressure  is  being  exerted  against  the 
side  of  a  cubical  vessel  when  full  of  water,  its  height 
being  18  inches?  Ans.  105.46+  Ibs. 

5.  How  much  pressure  would  be  exerted  upon!2sq. 
in.  of  the  sides  of  the  vessel  when  the  middle  point  of 
this  surface  is  20  inches  below  the  top  of  the  water  ? 

Ans.  8.68  Ibs. 

6.  How  many  cubic  inches  of  water  will  be  displaced 
by  a  piece  of  pine  wood  weighing  just  10  Ibs?     [See 
(13.)]  Ans.  276.48. 


NATURAL    PHILOSOPHY.  59 

7.  How  much,  less  will  a  piece  of  marble  measuring 
100  cubic  inches,  weigh  in  water  than  in  air  ?     [See 
(13.)]  Ana.  3.61  Ibs. 

8.  The  specific  gravity  of  marble  being  2.7,  what  will 
be  the  weight  of  25  cubic  ft.  ?         Ans.  4r218.75  Ibs. 

9.  How  many  cubic  inches  in  a  block  of  ice  that 
weighs  75  Ibs.  ?  A  ns.  2,229.12. 

10.  What  is  the  specific  gravity  of  flint  glass  if  a 
fragment  of  it  weigh,  in  air,  4,320  grs.,  and  in  water 
3,023  grs.  ?   t*  Ans.  3.33. 

11.  The  specific  gravity  of  wax  is  to  be  found  from 
the  following  data : — 

Weight  of  the  wax  in  air  -    -    -      8  oz. 
Weight  of  a  piece  of  lead  in  air     16  oz. 
Weight  of  the  lead  in  water  -    -    14.6  oz. 
Weight  of  wax  and  lead  in  water  13.712  oz. 

Ans.  0.9. 

12.  A  bottle  holding  l,000jgrs.  of  water  is  found  to 
hold  only  870  grs.  of-  oil  of  turpentine.     What  is  the 
specific  gravity  of  this  oil  ?  Ans.  0. 87. 

13.  How  much  pressure  can  be  exerted  upon   the 
large  piston  of  a  hydrostatic  press  by  applying  50  Ibs. 
to  the  small  piston  ;  the  area  of  the  small  piston  being 
J  sq.  in.,  that  of  the  large  piston  100  sq.  in.  ? 

Ans.  10,000  Ibs. 


§  4:.   OF  THE   PROPERTIES   OF   GASEOUS   BODIES. 

(16.)  The  most  characteristic  properties  of  gases  are 
compressibility  and  expansibility.  Besides  these  prop 
erties,  gases  possess  others  common  to  all  forms  of 
matter,  among  which  we  notice  elasticity  and  weight. 


60  NATURAL    PHILOSOPHY. 

1.  Compressibility. — Let  a  small  glass  tube  "be  fitted 
to  the  neck  of  a  vial  by  a  cork,  so  as  to  make  an  air- 
tight  joint.     "Warm   the   vial  gently,  and   then  put 
a   drop   of  ink   into   the  top   of  the   tube.     As   the 

Fig.  16.  vial  cools  the  drop  slowly  moves  down  the  tube 
until  it  finally  stops  at  some  point,  A  (Fig 
16).  There  it  will  be  held  by  the  capillary 
attraction  of  the  tube.  The  air  in  the  vial  and 
tube  up  to  the  point  A  will  thus  be  separated 
from  the  air  outside.  Now,  closing  the  upper 
end  of  the  tube  with  the  lips,  let  the  breath  be 
gently  pressed  against  the  drop;  it  will  be 
pushed  down,  it  may  be,  a  distance  of  several 
inches.  The  air  in  the  vial  can  not  escape,  and 
the  motion  of  the  drop  therefore  shows  that  the 
air  is  being  crowded  into  a  smaller  space,  in 
other  words,  that  it  is  compressible. 

2.  Expansibility. — If  the  vial  (Fig.  16)  be  warmed 
by  grasping  it  in  the  hand,  or  better,  by  standing  it  in 
warm  water,  the  drop  of  ink  will  move  upward  in  the 
tube.     The  air  in  the  vial  expands  and  pushes  the  drop 
along. 

Or  if,  through  the  cork  of  a  small  bottle,  a  glass  tube 
be  passed,  at  the  upper  end  of  which  is  a  bulb,  and  the 
lower  end  of  which  reaches  down  into  the  colored 
water  contained  in  the  bottle,  the  heat  of  a  lamp  flame 
may  be  applied  to  the  bulb.  It  will  be  noticed  that 
bubbles 'of  air  escape  from  the  lower  end  of  the  tube. 
The  air  is  expanded,  so  that  the  bulb  and  tube  can  no 
longer  hold  it  all. 

When  the  flame  is  withdrawn,  the  bulb  gradually 
<sools,  and  the  water  will  rise  in  the  tube  and  stand  at 
a  certain  height,  as  shown  in  Fig.  IT.  Now,  let 


NATURAL    PHILOSOPHY.  61 

the  palm  of  the  hand  be  laid  upon  the  bulb ;  the 
water  is  driven  down  the  tube  by  the  expand- 
ing air.  The  gentle  warmth  of  the  hand  is  quite 
sufficient  to  produce  a  very  considerable  expansior 
of  the  air. 

These  two  properties    belong  to   solid    and  PlK.  17% 
liquid  bodies  in  various  slight  degrees,  but  pre- 
eminently to  gases,  which  seem  to  be  compres- 
sible and  expansible  without  limit. 

The  force  of  heat  in  the  last  experiments  is  a 
repulsive  force  among  the  molecules  of  air,  and 
pushes  them  farther  apart.  As  long  as  this 
force  increases  by  the  action  of  the  flame,  it 
will  push  them  farther  and  farther  apart  con- 
tinually. In  the  first  experiment,  the  slight  press- 
ure of  the  breath  overcomes  the  repulsion  among 
the  molecules,  and  pushes  them  nearer  together. 
Should  the  pressure  be  increased,  we  can  give  no 
reason  why  the  molecules  should  not  continue 
to  approach  each  other.  The  limit  of  com- 
pressibility would  be  reached  when  the  molecules 
should  be  brought  into  actual  contact  with  each  other; 
but  to  do  this  would  doubtless  require  a  pressure 
immensely  greater  than  any  at  our  command. 

3.  Elasticity. — The  elasticity  of  air  is  beautifully 
shown  by  the  simple  apparatus  already  used  (see  Fig. 
16)  to  illustrate  the  characteristic  properties.     When 
the  breath  is  alternately  pressed  into  and  withdrawn 
from  the  tube,  the  air  will  alternately  be  compressed 
and  spring  back,  the  drop  of  ink  jumping  down  and 
up  ui  the  tube  to  show  it. 

4.  Weight. — The  air  has  weight.     If  we  would  show 
it,  we  may  first  weigh  an   open  vessel,  properly  ar* 


62 


NATURAL    PHILOSOPHY. 


ranged,  and  afterward  take  the  air  out  of  it  and  weigh 
it  again,  the  difference  in  these  two  weights  will  be  the 
weight  of  the  air  which  the  vessel  contains. 

But  how  can  the  air  be  taken  out  of  a  vessel  ?     To 
answer  this  question  we  must  become  acquainted  with 
Fig.  is.  the  air-pump.    A  section 

of  the  essential  parts  of 
this  important  instrument 
is  represented  in  Fig.  18. 

•^xx.  i  A  cylinder,  A  B,'is  joined 

(  \        Btifl          by  means  of  a  tube,  ~b  e,  to 

a  very  smooth  plate,  p.  A 
piston,  c,  moves  air-tight 
53  in  the  cylinder.  In  the 
piston  is  a  valve,  ?',  which 
opens  upward,  and  another  valve  at  &,  also  opens  up- 
ward from  the  tube  into  the  cylinder.  The  vessel,  d, 
from  which  the  air  is  to  be  taken  is  placed  upon  the 
plate.  Such  vessels  are  usually  called  receivers. 

It  will  be  seen  that  when  the  piston  is  raised,  the 
valve,  *,  will  be  closed,  and  the  air  above  it  will  be 
lifted  out  at  the  top  of  the  cylinder.  A  vacuum  would 
thus  be  formed  below  the  piston  were  it  not  for  the 
expansibility  of  the  air  in  the  receiver.  This  air  ex- 
pands, and  a  part  of  it  is  forced  through  the  valve,  5, 
into  the  cylinder.  "When  the  piston  is  pushed  down, 
the  air  below  it  passes  through  the  valve,  i,  and  when 
by  a  second  stroke  the  piston  is  lifted,  this  air  is  pushed 
out  at  the  top  of  the  cylinder,  while  another  portion 
from  the  receiver  is  pressed  through  the  tube  into  the 
cylinder  below  the  piston.  By  each  successive  stroke, 
the  quantity  of  air  in  the  receiver  is  diminished,  until, 
with  a  good  instrument,  the  quantity  left  will  be  almost 


NATURAL    PHILOSOPHY.  63 

inappreciable.  It  is  quite  evident,  however,  that  a 
perfect  vacuum  can  not  be  obtained  in  this  way.  One 
form  -of  this  important  instrument,  complete,  is  repre- 
sented in  Fig.  19. 

Fig.  19. 


We  may  now  attend  to  the  process  of  weighing  air.  A 
hollow  glass  globe,  with  a  stop-cock,  is  hung  from  one  pan 
of  a  delicate  balance,  and  its  weight  carefully  found.  It 
is  then  screwed  to  the  opening  in  the  plate  of  the  air- 
pump,  and  the  air  is  exhausted.  The  stop-cock  is  then 
closed  to  prevent  the  air  from  returning  into  the  globe, 
which  is  then  taken  from  the  pump  and  weighed.  It 
is  found  to  weigh  less  than  before,  and  the  difference 
must  be  the  weight  of  the  air  which  has  been  taken 
out.  At  the  ordinary  temperatures  of  air,  100  cubic 
inches  weigh  about  31  grains. 


64  NATURAL    PHILOSOPHY 


§  5.    OF   THE  PRESSURE   OF   THE   ATMOSPHERE. 

(JLT.)  The  atmosphere  exerts  pressure  in  all  direc 
tions.  This  pressure  is  about  15  Ibs.  upon  every  square 
inch  of  surface. 

1.  The  atmosphere  exerts  pressure. — Since  every  one 
hundred  cubic  inches  of  air  weigh  about  31  grs.,  it  is 
clear  that  the  atmosphere  must  be  exerting  considera 
ble  pressure  upon  the  surfaces  of  all  bodies  on  which 
it  rests. 

This  pressure  may  be  shown  in  various  ways.  Take 
a  glass  tube  of  convenient  length,  open  at  both  ends, 
and  insert  one  end  in  a  vessel  of  colored  water.  Apply 
the  lips  to  the  other  end,  and  as  the  air  is  drawn  out 
at  the  top,  the  water  will  rise  rapidly  in  the  tube. 
What  pushes  the  water  up?  The  ancients  called  it 
"Nature's  abhorrence  of  a  vacuum:"  many  at  the 
present  day  are  content  to  say  that  it  is  "  sucked  up." 
But  let  it  be  remembered  that  matter  never  moves  un- 
less it  is  forced  to  move,  and  that  the  forces  of  ab- 
horrence and  suction  are  simply  fictions.  The  only 
force  acting  upon  the  water  is  the  weight  of  the  air 
resting  on  its  surface  in  the  vessel.  This  downward 
pressure  pushes  the  water  under  the  lower  end  and 
upward  into  the  tube. 

A  more  beautiful  experiment  consists  in  causing  the 
pressure  of  the  air  to  produce  a  fountain  playing  in  a 
vacuum.  A  tall  glass  receiver  (Fig.  20)  is  closed  at 
the  bottom  by  a  stop-cock  which  terminates  in  a  tube 
extending  upward  a  little  way  into  the  receiver.  The 
air  from  this  receiver  being  taken  by  an  air-pump,  the 


NATURAL    PHILOSOPHY.  65 

stop-cock  is  immersed  in  a  vessel  of  water  and  opened. 
Instantly  the  water  leaps  to  the  top  of  the  receiver, 
and  a  beautiful  fountain  continues  to  play      Fig  20> 
until  the  jet  pipe  is  covered  by  the  falling 
water. 

2.  The  pressure  is  in  all  directions. — An 
experiment  easily  tried  will  show  that  the 
air  is    pressing   equally  in   all    directions. 
Stretch  a  piece  of  caoutchouc,  or  thin  india 
rubber,  over  the  large  end  of  a  lamp  chim- 
ney,  and  firmly   fasten   it   by   winding    a 
cord  around  it.     Apply  the  mouth  to  the 
other  end  of  the  tube  and  draw  the  air  out. 
The  pressure  of  the  air  pushes  the  rubber 
into  the  tube.     Hold  the  tube  in  any  po- 
sition, and  in  all  positions  the  rubber  will 
be  pushed  into  the  tube  alike. 

3.  The  pressure  is  15  Ibs.  to  the  square  inch. — If 
the  air  should  be  all  taken  out  of  our  tubes  used  in  the 
foregoing  experiments  [(IT.)  1],  the  water  would  en- 
tirely fill  them,  and  it  is  clear  that  the  pressure  of  the 
atmosphere  must,  at   least,  equal  the  weight   of  the 
water  in  the  tube.     How  much  farther  the  water  would 
rise  if  the  tube  was  long  enough,  these  experiments 
have  not  told.     A  heavier  liquid  will  not  be  lifted  as 
high  as  water,  and  will  be  more  convenient  for  experi- 
ment.    Mercury  is  a  liquid  metal  about  13^- times  as 
heavy  as  water,  and  it  is  found  that  the  air  will  sustain 
a  column  about  30  inches  high.     The  experiment  ia 
conducted  as  follows.     Take  a  glass  tube  more  than 
30  inches  long,  closed  at  one  end,  and  fill  it  with  mer- 
cury.    Close  the  open  end  with  the  finger  and  invert 
the  tube.     Now  place  the  open  end  in  a  dish  of  mer- 


NATURAL    PHILOSOPHY. 


cuiy  and  withdraw  the  finger.  It  will  be  seen  that 
Fig-  21.  the  top  of  the  column  of  mercury  in 
the  tube,  is  about  30  inches  above  the 
surface  of  the  mercury  in  the  dish. 
(Se^  Fig.  21.)  The  space  above  the 
mercury  in  the  tube  must  be  a  va- 
cuum. 

Now,  the  pressure  of  the  atmosphere 
just  balances  the  weight  of  this  column 
of  mercury.  The  weight  of  a  column 
of  mercury  30  inches  high,  the  area  of 
its  base  being  one  square  inch,  is  15 
pounds.  The  downward  pressure  of  the 
atmosphere  is  therefore  15  Ibs.  to  the 
square  inch  of  surface  on  which  it  rests. 

(18.)  The  principle  of  atmospheric 
pressure  is  applied  in  the  construction 
of  many  very  useful  instruments.  "We 
will  notice  the  barometer,  the  com- 
mon pump,  the  forcing  pump,  and  the 


siphon. 


I. THE   BAEOMETEE. 


A. — The  barometer  column  always  indicates  the  press- 
ure of  the  atmosphere.  But  the  pressure  of  the  at- 
mosphere depends  upon — 

1st.  Its  weight. 

2d.  The  amount  of  water-vapor  in  it. 

3d.  The  elasticity  of  its  lower  portions,  due  to  the 
action  of  heat. 

1     The  "barometer. — If  the  apparatus  used  to  deter- 


NATURAL,    PHILOSOPHY. 


67 


mint  the  pressure  of  the  atmosphere  (see  Fig.  21)  is 
inclosed  for  protection  in  a  frame  of  metal  or  wood, 
with  a  graduated  scale  attached,  to  measure  the  height 
of  the  column  of  mercury,  it  forms  the  instrument  so 
well  known  as  the  barometer. 

2.  Shows  the  pressure  of  the  atmosphere. — The 
pressure  of  the  atmosphere  is  not  always  the  same. 
When  it  is  less  than  15  Ibs.  to  the  inch,  the  column  of 
mercury  will  be  lower  than  30  inches,  and  when 
greater,  the  column  will  be  higher :  indeed  the  height 
of  the  column  will  vary  in  exact  proportion  to  every 
chango  in  the  pressure  of  the  air  which  supports  it. 
But  njtice  that  when  the  mercury  sinks  in  the  tube,  it 
must  ~ise  in  the  cistern,  and  that,  hence,  the  column 
must  shorten  at  both  ends,  while  the  figures  on  the 
scale  only  show  the  change  which  takes  place  at  the 
top  :  they  fail  to  tell  the  true  height  of  the  column. 

This  error  is  avoided  in  what  is  called  Fortin's  ba- 
rometer, by  means  of  a  cistern  with  a  flexible  bottom 
(see  Fig.  22).    The  bottom  of  this  cistern       Fig.  22. 
is  made  of  deerskin,  and  rests  upon  the  end 
ot  the  screw  C,  by  which  it  may  be  low- 
ered or  lifted.     An  ivory  pointer,  A,  is  fast- 
ened to  the  top  of  the  cistern,  and  its  lower 
end  is  the  point  from  which  the  distances 
are  measured  on  the  scale  which  shows  the- 
height  of  mercury  in  the  tube.     If  the  sur- 
face of  the  liquid  in  the  cistern  just  touches 
this  point,  then  the  figures  on  the  scale  show 
the  true  height  of  the  column,  which  indi- 
cates the  pressure  of  the  atmosphere. 

3.  The  pressure  of  the  atmosphere  depends  upon  ^ta 
weight. — Consider  the  atmosphere  as  a  vast  ocean  of 


68  NATURAL    PHILOSOPHY. 

air,  whose  depth  (or  height,  since  we  are  at  the  bottom: 
of  it)  is  thought  to  be  about  fifty  miles.  Its  upper  sur 
face  can  no  more  be  at  rest  than  can  the  surface  of  the* 
sea,  and  its  billows  must  be  more  immense,  because  ita 
substance  is  more  easily  moved.  The  barometer  ovor 
which  these  great  waves  sweep  to  and  fro,  being  now 
under  the  crest,  and  then  under  the  depression,  is  subject 
to  the  pressure  of  columns  of  air  of  different  heights, 
and  the  mercury  must  rise  or  fall  accordingly. 

Again ;  the  weight  of  the  atmosphere  will  vary  with 
the  altitude  of  the  place  where  the  observation  is  made. 
When  we  go  up  a  mountain-side,  we  leave  a  part  of 
the  atmosphere  below  us,  and,  of  course,  the  height 
of  the  column  above  us  is  less.  The  barometer  column 
will,  therefore,  be  shorter. 

Upon  this  principle  the  barometer  is  used  to  measure 
the  height  of  mountains.  If  the  density  of  the  atmos- 
phere were  uniform,  the  fall  of  the  mercury  would  be 
in  exact  ratio  of  the  distances  upward,  and  knowing  the 
height  required  to  make  the  mercury  fall  -^  of  an  inch, 
this  multiplied  by  the  number  of  tenths  through  which 
it  is  observed  to  sink,  would  tell  the  height  of  the  moun- 
tain. The  truth  is,  however,  that  the  density  of  the  air 
rapidly  diminishes  as  we  ascend.  Temperature,  too, 
affects  its  pressure.  In  spite  of  these  difficulties,  tables 
have  been  constructed,  by  which  the  height  of  a  place 
above  the  sea-level  may  be  calculated,  by  observing  the 
height  of  the  barometer  column  and  the  temperature 
of  the  atmosphere.  (See  Cooke's  Chein.  Phys.,  p.  511 ) 

4.  Upon  the  amount  of  water-vapor  it  contains.-  - 
Mixed  with  the  air,  at  all  times,  are  considerable  quan- 
tities of  invisible  vapor  of  water.  If  the  atmosphere 
was  pure  dry  air  alone,  it  would  exert  a  certain  press 


NATURAL    PHILOSOPHY. 


69 


ore:  if  it  consisted  wholly  of  water- vapor,  it  would 
exert  a  different  amount  of  pressure :  it  does  consist  of 
a  mixture  of  these  two  gases,  and  the  pressure  it  exerts 
is  the  sum  of  the  pressures  they  would  separately  ex- 
eit. 

It  follows  that  the  atmospheric  pressure  will  be 
greatest  when  there  is  the  greatest  quantity  of  water- 
vapor  in  the  air ;  the  barometer  column  will  then  rise. 
But  let  this  vapor  be  condensed  into  clouds,  and  it  will 
have  but  little  force  of  elasticity,  and  will  exert  but  a 
small  fraction  of  its  former  pressure ;  hence  the  barom- 
eter column  will  stand  lower  in  cloudy  weather. 

On  this  principle  the  barometer  is  used  to  indicate 
changes  in  the  weather.  A  rising  Fig.  23. 

column    indicates  fair    weather;    a 
falling  column  indicates  foul  weather. 

This  rule  is  to  a  great  extent  re- 
liable. Others  are  given  by  different 
observers,  but  they  must  be  taken 
with  considerable  allowance. 

5.  Upon  the  elasticity  of  its  lower 
portions. — Let  us  approach  this  topic 
by  means  of  an  experiment.  The 
tube,  A  B,  Fig.  23,  having  been 
filled  with  mercury  and  inverted, 
the  space  above  A  is  a  vacuum, 
and  the  column  of  mercury  is  sustain- 
ed by  the  pressure  of  the  air  at  B. 
Let  this  end  pass,  air-tight,  through 
ftie  stopper  in  the  lower  end  of  a  long 
glass  tube  C.  The  upper  end  of  this 
tube  is  ground  smooth,  and  covered 
with  a  heavy  grcund  glass  slide  S.  Now  let  the  tubo 


70  NATURAL     PHILOSOPHY. 

C,  be  heated.  The  air  within  is  expanded  ;  it  can  not 
escape  at  S  ;  *the  entire  expansive  force  is  exerted 
upon  the  mercury  at  B,  and  the  column  shows  this 
pressure  by  rising  at  A.  While  the  heat  is  continued, 
let  the  slide  S  be  drawn  so  as  to  leave  a  very  small 
hole  in  the  top  of  the  tube  C ;  a  gradual  fall  of  the 
mercury  at  A  will  show  that  the  pressure  of  the  air 
is  diminishing. 

Now  the  atmosphere  is  heated  by  coming  in  contact 
with  the  earth:  the  lower  stratum  is  heated  first,  and 
the  upper  strata  in  succession  afterward.  The  heated 
stratum  is  expanded  like  the  air  in  the  tube  C,  when 
heated.  It  attempts  to  rise,  but  the  strata  above,  not 
yet  heated,  rest  upon  it  and  prevent  its  rising,  just  as 
the  slide  S  keeps  the  air  in  our  tube,  and  the  expan- 
sive force  of  this  stratum  must  raise  the  barometer 
column.  This  expansive  force  will,  for  a  time,  increase, 
until  it  is  strong  enough  to  lift  the  weight  of  the  upper 
strata  of  air,  after  which  it  will  diminish,  just  as  it  did 
when  the  slide  S  was  removed. 

When  the  atmosphere  cools,  the  lower  stratum  is 
first  condensed,  and  this  allows  the  air  above  to  move 
downward.  In  falling  it  gains  a  certain  velocity,  and 
exerts  a  greater  pressure  :  the  barometer  column  must 
be  raised  thereby. 

We  see,  then,  that  as  the  atmosphere  is  daily  warmed 
and  cooled,  the  barometer  column  must  rise  and  fall. 
Observation  confirms  this.  From  nine  o'clock  to  ten  in 
the  morning,  the  mercury  reaches  its  greatest  height ; 
afterward  it  begins  to  fall,  and  at  three  or  four  in  the 
afternoon  it  reaches  its  lowest  point.  It  then  begins  to 
rise  again,  and  reaches  its  greatest  height  at  nine  or  ten 
in  the  evening.  These  motions  ocsur  every  day,  and 


NATURAL    PHILOSOPHY. 


71 


are  so  regular  that,  as  Humboldt  says,  they  might  be 
used  to  indicate  the  time  of  day,  only  that  the  distance 
through  which  the  column  fluctuates  is  very  small, 
being  greatest  at  the  equator,  where  it  amounts  to 
of  an  inch. 


n. THE   COMMON   PUMP 

This  instrument,  as  generally  made,  consists  of  two 
cylinders  or  barrels,  A  and   B,  Flg>  24 

Fig.  24,  with  a  valve,  S,  at  their 
junction,  opening  upward.  In 
the  upper  barrel  is  a  piston,  P, 
in  which  is  a  valve,  O,  also  open- 
ing upward.  The  piston  is  moved 
by  means  of  the  handle  II,  and 
the  water  may  flow  from  the 
Bpout  0. 

When  the  piston  is  lifted,  the 
air  above  it  will  be  lifted  out  of 
the  barrel.  A  partial  vacuum  will 
thus  be  formed  below  the  piston, 
and  the  pressure  of  the  air  upon 
the  surface  of  the  water  in  the 
well,  will  push  the  water  up  the 
barrel  A,  through  the  valve  S, 
into  the  barrel  B.  When  the 
piston  goes  down,  the  valve  S 
will  close,  and  prevent  the  return 
of  the  water  to  the  well.  The 
valve  in  the  piston  will  be  opened, 
and  the  water  will  pass  through  it.  When  the  piston 
is  again  lifted,  the  water,  now  above  it,  will  be  lifted  to 


72 


NATURAL    PHILOSOPHY. 


the  spout,  while  the   atmospheric  pressure  mil  force 
another  portion  into  the  barrel  below  the  piston. 

At  the  sea-le/el  the  pressure  of  the  air  will  sustain  a 
column  of  mercury  about  30  inches  high.  Since  mer- 
cury is,  at  ordinary  temperature,  about  13-J-  time? 
heavier  than  water,  the  same  force  will  lift  a  column  of 
water  13£  times  as  high:  13£x  30=405;  405  in.  =  33fft. 
The  lower  barrel  of  the  common  pump  must  not  exceed 
33f  ft.  in  length,  even  at  the  level  of  the  sea. 


IH. — THE   FORCING   PUMP. 

In  the  forcing  pump  the  piston  has  no  valve,  but 
from  near  the  bottom  of  the  upper 
barrel  there  is  a  tube  passing  to  an 
air-chamber,  with  a  valve  opening 
into  the  chamber.  A  section  of 
this  instrument  is  represented  in 
Fig.  25.  Reaching  from  near  the 
bottom  of  the  air-chamber  I  K,  is 
a  tube,  L  M,  which  extends  to  any 
place  at  which  the  water  is  to  be 
delivered. 

Now,  when  the  solid  piston  P, 
is  raised,  water  is  pressed  through 
the  valve  E,  into  the  barrel  B. 
When  the  piston  is  pushed  down  again,  the  water  is 
driven  through  the  tube  into  the  air-chamber,  and  com- 
presses the  air  in  it.  By  every  stroke,  the  water  accumu- 
lates in  the  chamber,  and  the  air  is  more  and  more  com- 
pressed. The  pressure  of  this  condensed  air  upon  the 
water  in  the  chamber,  pushes  it  up  through  the  tube 
L  M,  to  the  place  where  it  is  desired.  Without  the 


NATURAL    PHILOSOPHY.  73 

air-chamber,  the  water  would  issue  from  the  pipe  in 
jets ;  with  the  chamber,  the  water  issues  in  a  steady 
stream. 


IV. — THE   SIPHON. 

The  siphon  is  an  instrument  by  which  liquids  may 
oe  transferred  from  one  vessel  to  another,  by  atmos- 
pheric pressure.  It  consists  of  a  bent  tube,  one  arm  of 
which  is  longer  than  the  other.  In  Fig.  26,  the  si- 
phon in  operation  is  shown.  Having  been  first  filled 
with  water,  its  short  arm  Fig.  26. 

is  inserted  in  the  water  to 
be  transferred  from  the  ves- 
sel, C,  and  it  is  then  found 
that  the  water  will  flow 
steadily,  until  the  lower  end 
of  the  short  arm  is  left  un- 
covered, or,  in  other  cases, 
until  the  water  in  the  two 
vessels  stands  at  the  same 
level. 

Now,  the  downward  pres- 
sure of    the  air  at   C,    is 

partly  balanced  by  the  weight  of  the  column  of  water 
in  the  short  arm  of  the  tube  ;  the  excess  of  force  will 
tend  to  push  the  water  over  through  the  bend.  On  the 
other  hand,  the  atmospheric  pressure  at  B  is  partly 
balanced  by  the  weight  of  the  water  in  the  long  arm ', 
the  excess  will  tend  to  push  the  water  back  through  the 
bend  toward  C.  It  is  clear  that  the  pressure  of  air, 
minus  the  weight  of  the  shorter  column  of  water,  is 
more  than  the  same  pressure,  less  the  weight  of  the 


74  NATURAL    PHILOSOPHY. 

longer  column,  and  hence  that  a  greater  force  will  be 
exerted  to  push  the  water  from  C  toward  B,  than  from 
B  toward  C :  the  liquid  will  flow  in  the  direction  of 
the  greater  force. 

§  6.  OF  THE  RELATION  BETWEEN  THE  VOLUME  AND  THE 
WEIGHT  OF  AIB. 

(19.)  The  volume  of  any  given  weight  of  air,  or 
other  gaseous  body,  will  vary  with  every  change  in 
the  pressure  or  the  temperature  to  which  it  is  sub- 
jected. 

I. — PRESSURE. 

A. — The  volume  of  a  given  weight  of  air  will  be 
inversely  as  the  pressure  upon  it.  Hence  the  density 
of  the  atmosphere  is  greatest  at  the  surface  of  the 
earth. 

1.  Volume  inversely  as  the  pressure. — Press  the 
breath  into  the  tube  above  the  drop  of  ink  (see  Fig.  16), 
and  the  air  in  the  bottle  will  be  condensed.  Now  draw 
the  air  out  of  the  tube,  and  the  drop  rises,  showing  that 
the  air  below  has  expanded.  The  same  quantity  of  air 
is  here  seen  to  fill  less  space,  when  the  pressure  upon  it 
is  increased,  and  more  space  when  the  pressure  is 
diminished. 

Now,  we  may  prove  by  experiment,  first,  that  with 
a  double  pressure,  the  volume  will  be  just  one-half, 
and,  second,  that  with  half  the  pressure,  the  volume 
will  be  just  double. 

In  the  first  case,  we  use  a  bent  glass  tube  (Tig.  27), 


NATURAL    PHILOSOPHY. 


75 


the  short  arm  being  closed,  and  the  other,  which 
should  be  more  than  30  inches  long,  being  open 
at  the  top.  A  graduated  scale,  to  which  the  tube 
is  firmly  bound,  measures  inches  from  the  bend. 

Now,  let  mercury  be  poured  into  Fifr  27 

the  tube,  until  it  fills  the  bend.  The 
air  presses  upon  the  mercury  in  the 
long  arm,  and  this  liquid  transmits 
the  same  pressure  to  the  air  in  the 
short  arm.  The  pressure  upon  the 
air  in  the  short  arm  is,  therefore, 
15  Ibs.  to  the  square  inch.  If  we 
fill  the  long  arm,  as  shown  in  the 
figure,  to  the  height  of  30  inches, 
with  mercury,  we  will  be  adding 
a  pressure  of  15  Ibs.  to  the  inch. 
The  pressure  upon  the  air  in  the 
short  arm,  will  then  be  doubled,  and 
we  discover  that  the  mercury  has 
risen,  crowding  the  air  before  it,  and 
stands  at  A,  the  air  filling  just  half 
the  original  volume. 

In  the  second  case,  we  take  a 
glass  tube,  A  B  (Fig.  28),  about 
25  inches  long,  and  open  at  both 
ends.  Let  three  narrow  bands  of 
paper  be  pasted  upon  it,  one  at  a 
distance  of  3  inches  from  the  top, 
another  6  inches  from  the  top,  and  the  third  15  inches 
from  the  second.  Let  another  larger  tube,  D,  about 
30  inches  long,  be  nearly  filled  with  mercury.  Insert 
the  end  A,  of  the  small  tube  in  the  mercury  of  the 
other,  and  push  it  down  until  the  upper  mark  (3)  is 


76  NATURAL    PHILOSOPHY. 

at   the   level    of   the    mercury.     Now,  clasping    the 
finger  tightly  over  the  end  B,  thus  inclosing  3  inches 
Fig  28.         of   air   in    the   tube,  lift    it  until   the 
Bf\  third   mark    is  brought   up   to  the   top 

s  of  the  mercury.     The  air  will  be  found 

to  fill  the  space  of  6  inches. 

Before  the  tube  was  lifted,  the  pressure 
of  the  atmosphere,  15  Ibs.  to  the  inch, 
was  exerted  upon  the  air  in  it :  after  the 
tube  is  lifted,  the  atmosphere  sustains  a 
column  of  mercury  15  inches  high.  To 
do  this  takes  half  the  pressure  it  can 
/S  exert,  the  other  half  is  exerted  upon  the 
air  above  the  mercury.  We  thus  show 
that  with  half  the  pressure  the  volume 
will  be  just  double. 

From  these  two  experiments  we  infer 
that  the  volume  of  a  given  weight  of  air 
will  ~be  inversely  as  the  pressure  upon  it, 
and  repeated  experiment  confirms  the 
inference. 

This  law  was  discovered  by  the  Abbe 
Mariotte  in  France,  and  is  generally  called  Mariotte's 
law,.  (See  Cooke's  Chem.  Phys.,  p.  287.) 

2.  The  density  of  the  atmosphere. — When  a  given 
weight  of  air  is  crowded  into  one-half  its  original  vol- 
ume, it  must  be  twice  as  dense ;  and  when  expanded 
into  double  its  first  volume,  it  can  only  be  half  as  dense. 
The  density  of  air  will  therefore  be  exactly  in  propor- 
tion to  the  pressure  upon  it.    So  the  atmosphere,  where 
its  pressure  is  greatest,  will  be  most  dense. 

3.  Is  greatest  at  the  surface  of  the  earth. — The  at- 
mosphere in  contact  with  the  earth  is  pressed  upon  by 


NATUEAL    PHILOSOPHY.  77 

ail  the  air  above,  even  to  the  top  of  the  atmosphere. 
At  a  distance  above  the  earth,  the  atmosphere  receives 
less  pressure,  because  there  is  less  air  above  to  exert  it, 
The  density  being  greatest  where  the  pressure  is  great- 
est, the  air  at  the  surface  must  be  more  dense  than 
the  portions  above.  The  air  is  much  less  dense  at  the 
top  of  a  high  mountain  than  at  its  base. 

II. TEMPERATURE. 

JB. — The  volume  of  a  given  weight  of  air  will  be 
greater  as  its  temperature  is  higher.  It  expands  ^fa 
of  its  bulk  for  every  additional  degree  of  heat. 

1.  Heat  increases  the  volume  of  air. — Let  the  palm 
of  the  hand  be  laid  upon  the  bulb  (Fig.  IT),  and  the 
fluid  in  the  tube  descends,  because  the  air  in  the  bulb 
expands.      Pour  cold  water  upon  the  bulb,  and  the 
fluid   ascends  because  the  air  above  it  is  condensed. 
Apply  the  heat  of  the  lamp  flame  to  the  bulb,  and 
the  water  in  the  tube  will  be  quite  driven  out  at  the 
bottom :  let  it  cool  again,  and  the  water  rises  to  its 
former  height.    These  experiments  show  that  the  addi- 
tion of  heat  expands  air,  and  that  its  withdrawal  con- 
tracts it. 

2.  At  the  rate  of  Tiir  its  bulk  for  each  degree. — The 
expansion  of  air  and  other  gases  by  heat,  is  uniform. 
One  degree  of  heat,  when  the  temperature  is  low,  pro- 
duces the  same  expansion  as  one  degree,  when  the  tem- 
perature is  high.     If  we  have  490  cubic  inches  at  a 
temperature  of  32°,  it  will  become  491  cubic  inches  if 
heated  one  degree,  making  its  temperature  33°.     In 
other  words,  it  expands  -^^  of  its  bulk  at  32?,  for  each 
additional  degree  of  heat  applied. 


78  NATURAL    PHILOSOPHY. 

PROBLEMS    ILLUSTRATING-   THE   LAWS    OF    GASEOUS    BODIES, 

1.  What  is  the  weight  of  a  cubic  foot  of  air  at  ordi- 
nary temperature  and  pressure? 

Ans.  535.68  grs. 

2.  What  is  the  weight  of  100  cub.  in.  of  oxygen  gaa 
at   ordinary    temperature    and   pressure,   its    specific 
gravity  being  1.108  ?  Ans.  34.348  grs. 

3.  What  is  the  weight  of  100  cub.  in.  of  nitrogen 
gas  at  ordinary  temperature  and  pressure,  its  specific 
gravity  being  .972  ? 

4.  Wluit  pressure  will  be  exerted  by  the  atmosphere 
on  a  surface  of  1  sq.  ft.  ?    [See  (IT.)]     Ans.  2,160  Ibe. 
'  5.  What  pressure  does  the  atmosphere  exert  upon  a 
square  inch   surface   when  the  barometer  column  is 
28  inches  high  ?     [See  (18.)  A.  2.]  Ans.  14  Ibs. 

\r  6.  How  hig^  a  column  of  water  would  the.  atmos 
phere  sustain  when  the  barometer  column  stands  at  a 
height  of  28  inches  ?  ..  iv,.«  Ans.  31|  ft. 

*   7.  Suppose  100  cub.  in.  of  air  at  a  pressure  of  15  Ibs. 
to  the  inch  is  made  to  receive  an  additional  pressure 
of  15  lbs.*ta  the  inch,  what  will  be  its  Volume  ?     [See 
V%V(19.)A.]   Y  ,  Ans.  50  cub.  in. 

8.  How  much  pressure  must  be  removed  from  100 
cub.  in.  of  air,  at  usual  density,  in  order  that  it  may 
expand  to  a  voliime*  of  20Q  cub.  in.  ? 

^  .  v.  e  Ans.  7J  Ibs.  to  the  inch. 

9.  In  the  air-chamber  of  the  forcing-pump,  the  air  is 
compassed  into  half  its  former  bulk- ;  how  high  will  the 
water  be  thrown  ?  Ans.  33f  ft. 

•  10.  If  we  have  500  cub.  in.  of  air  at  32°  temp., 
how  much  will  there  be  when  it  is  heated  to  a  tem- 
perature of  75°  ?  [See  (19.)  B.]  Ans.  543.88+  cub.  in 


PAET    II. 

THE  PHENOMENA  OF  BODIES  IS  MOT10K 


v- 


NATURAL    PHILOSOPHY.  81 


CHAPTER    III. 


OF  MOTION. 

INTRODUCTION. APPLICATION    OP     THE     FUNDA- 
MENTAL    IDEAS. 

(20.)  Read  (4.)  and  (7.) — Attraction  and  repulsion 
acting  upon  masses  of  matter  determine  their  con- 
dition of  rest  or  motion. 

1.  The  motion  of  bodies  falling  to  the  ground  is  due 
to  the  attraction  of  gravitation.  The  motion  of  air  in 
wind  is  caused  chiefly  by  the  repulsive  power  of  heat. 
The  bullet  speeds  on  its  mission  of  death,  urgqd  by  the 
repulsive  force  of  exploding  gunpowder.  The  forces 
which  produce  the  endless  variety  of  motions  in  nature 
are  found,  when  carefully  studied,  to  be  only  different 
forms  of  attraction  and  repulsion. 

We  speak  of  the  forces  of  nature,  and  call  them 
wind,  water,  gravitation.  This  is  well,  because  these 
names  have  been  given  to  familiar  forms  of  force.  "We 
will  continue  to  use  these  terms  :  at  the  same  time,  le" 
us  do  justice  to  the  simplicity  of  God's  stupendou 
works,  by  remembering  that  the  forces  of  nature  are 
attraction  and  repulsion. 

4* 


52  NATURAL    PHILOSOPHY. 

§  1.    OF   MOTION   CAUSED   BY    A   SINGLE   FORCE. 

(21.)  There  are  three  important  principles  called  the 
laws  of  motion  : — 

1st.  A  body  at  rest  will  remain  at  rest ;  or,  if  in  mo- 
tion, it  will  move  forever  in  a  straight  line,  unless  acted 
upon  by  some  force  to  change  its  condition. 

2d.  A  given  force  will  produce  the  same  amount  of 
motion,  whether  it  act  upon  a  body  at  rest,  or  in  motion. 

3d.  Action  and  reaction  are  equal,  and  in  opposite 
directions. 

1.  The  first  law. — The  first  law  is  proved  when  we 
remember,  that  the  inertia  of  matter  forbids  that  a  body 
shall,  in  any  way,  change  its  own  condition. 

Then,  why  are  bodies  so  constantly  changing  their 
condition  of  rest  or  motion  ?  Who  ever  saw  a  body  in 
nature,  moving  in  an  absolutely  straight  line  ?  Bodies 
are  constantly  under  the  influence  of  forces  which  do 
change  their  condition.  A  stone  thrown  from  the  hand 
would  move  forever  in  a  straight  line,  if  it  felt  only  the 
force  of  the  hand;  but  gravitation,  and  the  resistance  of 
the  air,  compel  it  to  move  in  a  graceful  curve  instead. 
The  pleasing  variety  of  natural  motions  is  brought 
about  by  the  unceasing  action  of  external  forces. 

2.  The    second  law. — Let  us   examine  this  law  by 
means  of  the  diagram,  Fig.  29.    If  a  ball  be  thrown  sud- 
denly from  the  point  A,  horizontally,  it  would  go  to 
the  point  B,  if  it  could  be  let  alone  by  other  forces.     So 
likewise  if  it  be  dropped  from  A,  gravitation  alone  will 
carry  it  to  0.     Now,  these  separate  effects  of  the  two 
forces  will  be  exactly  produced  when  the  forces  act  to- 
gether.    Suppose  the  ball  to  go  from  A  to  B  in  one 


NATURAL    PHILOSOPHY. 


83 


minute,  and,  when  dropped,  to  fall  from  A  to  C  in  the 
same  time.  *N"ow,  while  the  ball  is  moving  toward  B, 
gravitation  is  pulling  it  downward,  and  at  the  end  of 
the  minute  it  will  be  found  at  D,  having  moved  to  the 
right,  a  distance  exactly  equal  to  A  B,  and  downward 


Fig.  29. 


Fig.  30. 


through  a  distance  exactly  equal  to  A  C ;  so  that  the 
force  of  gravitation  produces  the  same  effect,  whether  it 
act  upon  the  ball  resting  at  A  or  in  motion  toward  B. 
3.  The  third  law. — If  a  table  be  struck,  the  hand 
that  strikes  it  receives  a  blow  as  well.  The  hand  acts 
upon  the  table ;  the  table  reacts  upon  the  hand.  At- 
tend, no-r>  to  the  following  experiment.  Two  ivory 
balls  are  suspended  by 
cords,  and  hang  in  con- 
tact against  a  grad- 
uated arc.  When  the 
ball,  B,  is  lifted  up  the 
arc  to  D,  and  then  al- 
lowed to  swing  against 
the  other,  it  strikes  it 
and  instantly  stops, 
while  the  other  ball 
takes  up  its  motion, 
and  goes  to  the  point  0.  The  first  ball  acts  upon  the 


84  NATURAL     PHILOSOPHY. 

second ;  the  second  reacts  upon  the  first.  Now,  if  we 
notice  that  the  motion  from  D  to  B,  which  is  stopped 
by  the  reaction  of  the  second  ball,  is  just  equal  to  the 
motion  from  A  to  C,  which  is  caused  by  the  action  of 
the  first,  it  becomes  evident  that  the  two  forces  must 
be  equal,  and  exerted  in  opposite  directions. 

It  follows  from  this  principle  that,  when  two  bodies 
come  in  contact,  each  one  gives  and  receives  an  equal 
shock.  The  hand  which  strikes  the  table  is  itself 
bruised,  and  the  bullet  which  shatters  the  bone,  is  itself 
battered  and  torn. 

(22.)  The  velocity  of  a  moving  body  will  be  uniform 
if  it  be  produced  by  an  impulsive  force  and  opposed  by 
no  resistances. 

The  elements  of  motion  are  time,  space,  and  velocity. 
In  uniform  motion,  the  space  is  equal  to  the  product  of 
time  multiplied  by  velocity. 

1.  Velocity. — Telocity,  in  a  popular  sense,  is  simply 
rapidity  of  motion,  but  if  the  term  is  to  be  of  any 
scientific  value   it   must  be  more  definitely  applied. 
Telocity  is  the  distance  passed  over  by  a  body  in  a 
unit  of   time.     The  velocity  of  a   cannon  ball,   for 
example,  may  be  2,000  ft.  a  second :  that  of  a  train  of 
cars  may  be  30  miles  an  hour. 

2.  Uniform  velocity. — In  uniform  velocity,  a  body 
moves  over  equal  spaces  in  equal  times.    If,  for  instance, 
in  each  of  three  successive  hours,  a  steamboat  travels  15 
miles,  its  velocity  is  uniform. 

3.  An  impulsive  force. — An  impulsive  force  is  one 
which,  after  acting  for  a  time,  ceases.     The  stroke  of 
a  bat,  which  knocks  the  ball,  is  an  impulsive  force; 
so    are   the  blows   of  a  hammer.    No  matter  how 


NATURAL    PHILOSOPHY.  g5 

long  a  force  may  have  been  acting,  if  it  be  sud- 
denly withdrawn,  it  is  at  that  moment  an  impulsive 
force. 

4.  Uniform  motion  produced  by  an  impulse. — If 
a  body  can  be  free  from  all  forces  but  the  impulse  which 
gives  it  motion,  its  velocity  will  be  uniform.     This 
eeldom  occurs.     How  rarely  do   we   see    a  uniform 
motion  produced  by  an  impulse,  either  in  nature  or  in 
art !     It  is  because  all  bodies  are  under  the  influence 
of  several  forces  at  once,  such  as  gravitation,  friction, 
and  the  resistance  of  air,  by  which  their  velocities  are 
changed.     The  motion  of  the  earth  on  its  axis  is,  how- 
ever, a  sublime  example  of  uniform  motion. 

In  the  arts,  a  uniform  motion  can  be  secured  only 
by  the  constant  application  of  power.  The  impulse 
which  starts  a  train  of  cars,  would  make  it  move  uni- 
formly if  it  did  not  meet  with  resistances :  to  overcome 
these,  a  constant  pressure  of  the  steam  must  be  applied. 
If  this  pressure  be,  at  all  times,  just  equal  to  the  pur- 
pose, the  motion  of  the  train  will  be  uniform. 

5.  Space    equals   time    multiplied  by   velocity. — It 
is   evident  that  a  train   of  cars,  going  uniformly  at 
the  rate  of  25  miles  an  hour,  will,  in  ten  hours,  go  250 
miles :   250  =  25  x  10,  or  the  space  is  equal  to  the 
product  of  the  two  other  elements,  time  and  velocity. 

We  may  express  this  principle  by  the  simple  equa- 
tion— 

S  =  T  x  Y:  in  which 
S  stands  for  Space. 
T    «       "    Time. 
Y    "       «    Yelocity. 

Now,  if  any  two  of  these  elements  are  given,  the 
third  may  be  found  by  substituting  given  values  for 


gfl  NATURAL    PHILOSOPHY. 

the  letters,  and  then  performing  the  operations  indi- 
cated.  For  example,  what  is  the  velocity  of  a  bullet 
which  goes  2,000  ft.  in  20  seconds,  supposing  its  velo- 
city uniform?  The  value  of  S  is  2,000ft.;  the  value 
of  T  is  20  seconds.  Putting  these  values  in  the  equa- 
tion, it  becomes 

2,000  =  20  x  V.     Hence  Y  =  100. 

(23.)  The  motion  of  a  body  produced  by  the  action 
of  a  constant  force  alone,  will  be  uniformly  accelerated. 
The  difficulties  in  the  way  of  any  accurate  experiment 
upon  uniformly  accelerated  motion  are  overcome  by 
Atwood's  machine. 

1.  A  constant  force. — By  a  constant  force  we  mean 
a  force  which  acts  upon  a  moving  body  all  the  time 
alike.     The  force  of  gravitation  is  the  most  perfect 
example  of  a  constant  force. 

2.  Uniformly  accelerated  motion. — The   motion  of 
a  body  is  uniformly  accelerated,  when  its  velocity  in- 
creases equally  in  successive   units  of  -time ;    as,   for 
example :  5  ft.  the   first  second,  8  ft.  the  next  second, 
lift,  the  third  second,  14ft.  the  fourth,  and  so  on. 

The  motion  of  a  falling  body  is  the  most  perfect 
example  of  uniformly  accelerated  motion.  It  would 
be  a  perfect  example  were  it  not  for  the  resistance  of 
the  air. 

3.  Difficulties   in   the  way    of  experiment. — Three 
difficulties  are  in   the   way  of   accurate   experiments 
upon  the  motion  of  a  body  falling.     1st.   It  is  so  rapid 
that  no  accurate  observations  can  be  made.     2d;  It  is 
subject  to  the  resistance  of  air,  which  reduces  its  veloc- 
ity.    3d.  The  frictior  of  any  apparatus  used  is  likely 
to  impede  it 


NATURAL    PHILOSOPHY. 


4.  These  diffi- 
culties overcome 
by  AtwoocPs  ma- 
chine.— These  dif- 
ficulties are,  for 
the  most  part,  over- 
come by  Atwood's 
machine  (Fig.  31). 
Two  heavy  weights 
A  and  B,  are  fast- 
ened to  the  ends 
of  a  small  cord 
which  passes  over 
a  grooved  wheel, 
D.  Each  end  of 
the  axis  of  this 
wheel  rests  on  the 
circumferences  of 
two  other  wheels. 
The  standard  L,  is 
graduated  :  upon 
it  is  a  movable 
ring,  C,  which  al- 
lows the  weight 
A  to  pass  through 
it,  and  a  table  be- 
low, which  arrests 
the  motion  of  the 
weight  at  any  de- 
sired point.  The 
time  of  motion  is 
measured  by  the 
pendulum  F. 


Fig.  81. 


88  NATURAL    PHILOSOPHY. 

The  two  weights  A  and  B  are  made  exactly  equal,  and: 
of  course,  when  left  to  themselves,  will  remain  at  rest. 
But  if  a  small  bar  of  brass  be  laid  upon  the  weight 
A,  motion  takes  place,  due  entirely  to  the  action  of 
gravitation  upon  the  bar. 

Now,  suppose  the  large  weights  each  to  be  31J  oz., 
and  the  weight  of  the  small  bar  to  be  1  oz.  "When 
they  all  move,  64  oz.  are  in  motion,  caused  by  the  force 
which  acts  upon  the  1  oz.  bar.  It  is  evident  that  64  oz. 
will  move  only  -$?  as  fast  as  1  oz.,  with  the  same 
force.  The  motion  of  the  weights  is  produced  by  a 
constant  force,  gravitation ;  but  it  is  only  ^  as  rapid  as 
when  the  bodies  fall  freely.  A  slow  motion  is  thus  ob- 
tained. The  resistance  of  the  air  against  the  small 
surfaces  of  the  ends  of  the  heavy  weights,  is  very  slight 
when  they  move  slowly ;  the  friction  of  the  wheels  at 
the  top  is  trifling,  and  thus  the  three  difficulties  in  the 
way  of  experiment  are  overcome. 

(24.)  By  experiments  with  Atwood's  machine  we 
may  prove : — 

1st.  That  a  body  moving  under  the  influence  of  gravi- 
tation during  any  interval  of  time,  will  gain  a  velocity 
which,  acting  alone,  will  carry  the  body  twice  as  far  in 
the  next  equal  interval. 

2d.  That  gravitation  will  add  to  the  motion  of  a  body 
just  as  much  in  every  interval  of  time  as  it  produced 
in  the  first. 

By  the  help  of  these  principles  we  may  analyze  the 
motion  of  a  falling  body.  From  the  diagram  which 
represents  this  analysis,  we  may  construct  a  table  which 
shall  contain  the  values  of  time,  space,  and  velocity ; 
and  from  this  table  obtain  the  laws  which  govern  the 


NATURAL    PHILOSOPHY.  89 

motion,  and  the  formulas  by  which  problems  may  be 
solved.     (See  Cooke's  Chem.  Phys.,  p.  23.) 

1 .  Proof  of  the  first  principle. — Let  the  weight  A, 
carrying  the  small  bar,  be  brought  to  the  top  of  the 
graduated  standard.     Suppose  that,  in  one.  second  after 
its  release,  it  falls  to  the  ring  0,  a  distance  of  3  inches. 
The  small  bar  will  be  caught  off  by  the  ring ;  the  weight 
A  will  pass  through,  and  in  the  next  second  it  will  be 
found  to  go  exactly  6  inches.     By  putting  the  ring  at 
different  places  on  the  standard,  it  will  be  found  that, 
in  every  case,  as  in   the  one  just  described,  the  ~body 
moving  under  the  influence  of  gravitation  during  any 
interval  of  time,  will  gain  a  velocity  which,  alone,  will 
carry  the  body  twice  as  far  in  the  next  equal  interval. 

2.  Proof  of  tlie  second  principle. — If  the  weight  and 
bar  fall  3  inches  in  one  second,  they  will  be  found  to 
fall  12  inches  in  two  seconds.     The  distance  fallen  in 
the  second  interval  is  9  inches.     If  the  bar  were  taken 
off  at  the  end  of  the  first  second,  the  weight  would  go 
alone,  6  inches  in  the  next.     It  is  clear,  then,  that  the 
bar  acting  in  the  last  second  adds  a  motion  of  3  inches, 
the  same  amount  as  it  produced  in  the  first.     Eepeated 
experiments  show  that  gravitation  will  add  to  the  mo- 
tion of  a  falling  "body  just  as  much  in  each  second  as 
it  produced  in  the  first. 

3.  Analysis  of  the  motion  of  a  falling  ~body. — Now 
suppose  a  body  to  fall  from  the  point  A  (Fig.  32),  tor 
ward  the  point  D.     In  the  first  second  it  will  fall  a 
certain  distance,  which  we  will  represent  by  A  B.     For 
a  moment  suppose  the  force  of  gravity  should  ceast, 
to  act,  the  body  would  still  move  on,  and  we  know 
(by  the  first  principle),  that  it  would  go  in  the  next 


90  NATURAL    PHILOSOPHY. 

second,  just  twice  as  far  as  it  did  in  the  first.  Then 
mark  below  B,  two  spaces,  each  equal  to  A  B,  to 
represent  this  distance,  and  mark  it  with  a  heavy  line, 
that  the  eye  may  see  at  a  glance,  that  it  is  the  distance 
due  to  velocity  alone.  But  we  know  (by  the  second 
Fi  82  principle)  that  gravitation  in  this  second  will 
add  a  space  just  equal  to  A  B.  Marking  this 
space  in  the  figure,  we  find  that  in  two  seconds 
the  body  will  fall  to  C. 

In  two  seconds  the  body  has  fallen  4  spaces, 
in  the  next  two  seconds  it  will  go  twice  as  far, 
8  spaces,  by  velocity  alone.  In  the  first  of  these 
two  seconds,  which  is  the  third  second  of  its 
fall,  the  body  will  go  4  spaces  by  velocity. 
The  force  of  gravity  adds  another  space,  so 
that  at  the  end  of  3  seconds  the  body  will  be 
found  at  D. 

To  find  the  distance  passed  in  the  4th  sec- 
ond, notice  that  in  the  first  3  seconds  it  has 
passed  9  spaces ;  that  in  the  next  3  seconds  it 
will  go,  by  its  velocity  alone,  18  spaces,  and 
that  in  one  of  these  3  seconds,  which  would 
be  the  4th  second,  it  would  go  6  spaces. 
Mark  6  spaces  for  velocity,  and  add  one  for 
the  action  of  gravitation. 

4.   Construction  of  the  tal)U. — ^N~ow,  in  this 


•  diagram  the  values  of  time, 
space  and  velocity  stand 
clearly  before  us,  and  we 
may  put  them  in  a  tabular 
form.  In  the  first  column, 
headed  T,  put  the  number 


T. 


S. 


4      16<7     8<7      1g 


of  seconds,  1,  2,  3,  4.     In  the  second  column, 


NATURAL     PHILOSOPHY,  91 

headed  S,  put  the  total  space  passed  over  at  the 
end  of  these  seconds,  representing  the  distance  A  B 
by  g.  In  the  third  column,  headed  V,  put  the  veloci- 
ties gained  at  the  end  of  each  of  the  seconds.  And, 
finally,  in  the  fourth  column,  headed  s,  put  the  spacea 
passed  in  each  separate  second. 

5.  From   the   table  obtain  the  laws. — The  relation 
between  time,  space,  and  velocity,  may  be  seen  by  com- 
paring their  values  given  in  this  table. 

[Notice,  first,  that  the  values  of  S  have  the  same 
ratio  as  the  squares  of  the  value  of  T.  For  instance, 
take  the  spaces  4g  and  9<?  with  the  corresponding  times 
2  and  3,  we  find  that  4#  :  9$  : :  22  :  3*.  Hence,  the 
spates  passed  In/  a  falling  body  in  different  times  are 
as  the  squares  of  the  times. 

Notice,  second,  that  the  values  of  V  have  the  same 
ratio  as  the  values  of  T.  Thus  we  find  that  the  -ve- 
locities, 4g  and  6*7,  have  the  same  ratio  as  2  and  3,  the 
corresponding  values  of  time.  Hence,  the  velocities  of 
a  falling  body  at  the  end  of  successive  intervals  of  tim# 
will  vary  as  the  time  of  fall. 

Notice,  third,  that  the  spaces  passed  in  separate 
seconds  (the  values  of  s)  are  as  the  odd  numbers,  1,  3, 
5,  7,  &c. 

6.  From   the   table    also    obtain   the  formulas. — :lt 
will  be  seen  that  by  squaring  any  one  of  the  values  of  T 
in  the  table,  and  then  multiplying  by  g,  the  correspond- 
ing value  of  S  will  be  obtained.     Hence, 

S  =  TV  (1). 

A  gain,  we  may  discover  that  if  the  value  of  T  in  any 
case  be  multiplied  by  2g  the  corresponding  value  of  V 
will  be  produced.  Hence, 

Y  =  2/T  (2). 


92  NATURAL    PHILOSOPHY. 

"We  see,  again,  that  if  the  value  of  S  in  any  case  be 
multiplied  by  </,  the  square  root  of  this  product  multi- 
plied by  2,  gives  the  value  of  Y.  Hence, 


Finally,  a  little  attention  will  show,  that  if  the  value 
of  T  in  any  case  be  multiplied  by  2,  the  product  di- 
minished by  1,  and  the  remainder  multiplied  by  g,  the 
corresponding  value  of  s  will  be  obtained.     Hence, 
«  =  (8T-  1)<7(4). 

7.  By  these  formulas  solve  problems.  —  By  the  use  of 
these  four  formulas  all  problems  in  uniformly  accele- 
rated motion  may  be  solved.  In  all  cases,  g  represents 
the  distance  passed  by  the  body  in  the  first  interval  of 
time.  Its  value  will  be  different  for  different  forces. 
When  gravitation  is  the  constant  force  which  causes 
the  motion,  the  value  of  g  is  16-^  f66^ 

A  single  illustration  will  show  how  the  formulas 
may  be  used.  If  a  stone  be  dropped  into  a  well  whose 
mouth  is  144J  ft.  above  the  water,  how  long  will  it 
take  to  reach  the  water  ?  Since  gravitation  produces 
this  motion,  the  value  of  g  is  16^-  ft.  The  14:4rf  ft.  is 
the  value  of  S,  and  the  value  of  T  is  required.  The 
relation  between  these  elements  is  expressed  by  the 
formula  S  =  T2<7,  and  by  substituting  the  given  values 
we  have  144f  =  T2  x  16^.  The  value  of  T,  from  this 
equation  is  3  seconds. 

PROBLEMS    ILLUSTRATING     THE     LAWS    OF    MOTION    WHEN 
PRODUCED   BY   A    SINGLE   FORCE. 

1.  A  body  moves  uniformly  over  a  distance  of  780 
feet  with  a  velocity  of  5  feet  a  second  :  in  what  time 
did  it  go  ?  Am.  156  sec. 


NATURAL    PHILOSOPHY.  93 

ts  2.  Under  the  influence  of  an  impulsive  force,  a  body 
moves  at  the  rate  of  25  feet  a  second :  how  far  will  it 
go  in  one  minute  ? 

3.  A  stone  dropped  from  the  top  of  a  tower,  struct 
the  ground  in  4  seconds :  how  high  is  the  tower  ? 

^LTIS.  257-J-  feet. 

4.  If  the  tower   were   257-J-   feet  high,  with   what 
velocity  would  a  stone  strike  the  ground? 

^Lws.  128f  feet. 

5.  If  the  velocity  of  the  stone  should  be  128f  feet 
a  second;  how  long  a  time  had  it  been  falling  ? 

J.w<9.  4  sec. 

s  6.  A  body  falls  4  seconds :  how  far  does  it  go  in  the 
fourth  second  ?  ^?w?.  112^  feet. 

S  1.  Under  the  influence  of  a  constant  force,  a  body 
moves  3  feet  the  first  second :  how  far  will  it  go  in  5 
seconds  ?  Ans.  75  feet. 

8.  A  body  is  falling  toward  the  earth ;  it  is  at  the 
same  time  moving  horizontally  under  the  influence  of 
a  constant  force  which  made  it  go  10  feet  in  the  first 
second :  how  far,  horizontally,  did  it  go  in  8  seconds  ? 
[See  (21.)  2.]  Ana.  640  feet. 

9.  How  far  did  it  fall  in  the  same  time  ? 

Ans.  1,029J-  feet- 

Y'  10.  With  what  velocity  did  it  strike  the  ground  ? 

Ans.  257J  feet. 

*/  11.  What  velocity  did  it  gain  in  a  horizontal  direc- 
tion ?  Ans.  160  feet. 
12.  How  far  did  it  go  horizontally  in  the  5th  second  1 

Ans.  90  feet. 
¥  13.  How  far  did  it  fall  in  the  5th  second  ? 

Ans.  144f  feet. 
14.  Under  the  influence  of  a  constant  force,  a  body 


94:  NATURAL    PHILOSOPHY. 

goes  12  feet  in  the  first  3  seconds ;  now  far  does  it  go 
in  IS  seconds?  Ana.  432  ft. 

15.  A  ball  is  thrown  directly  upward,  starting  with 
a  velocity  of  96  J  feet,  to   what  height  will  it  rise  \ 

Ans.  144f  ft. 

The  motion  of  this  ball  thrown  upward,  will  be 
retarded  by  gravitation,  in  exactly  the  same  ratio  that 
it  is  accelerated  in  falling  to  the  ground  again.  The 
height  to  which  it  rises  is  the  same  as  that  from  which 
it  falls.  This  problem  may  be  solved  exactly  as  if  the 
question  were :  from  what  height  would  the  ball  fall 
to  gain  a  velocity  of  96  j-  feet  a  second  ? 

16.  A  ball  is  shot  upward  with  a  velocity  of  386 
feet :  how  long  will  it  continue  to  rise  ?    Ans.  12  sec. 

17.  How  high  does  it  go  ?  Ans.  2,316  ft. 

18.  How  long  does  it  remain  in  the  air  ? 

Ans.  24  sec. 

19.  How  far  does  it  rise  in  the  last  second  of  its 
ascent  ?     .  Ans.  16TV  ft. 

20.  How  far  does  it  fall  in  the  last  second  of  its  de- 
scent ?  Ans.  369{^  ft. 

21.  Suppose  the  large  weights  of  Atwood's  machine 
to  be  each  31£  oz.,  and  the  weight  of  the  small  bar  to 
be  1  oz.     We   find,  by  experiment,  that  the  weight 
and  bar  go  3  inches  in  the  first  second :  what  is  the 
force  of  gravity,  or,  in  other  words,  how  far  would  grav- 
itation  cause   a   body   moving  freely  to  fall  in  one 
second  ? 

In  this  case,  the  whole  weight  moved  by  the  force  of 
gravitation  on  the  bar,  is  31i| +31i-+l  =  64oz.  It  is 
clear  that  64  oz.  will  move  only-g^  as  far  in  one  second 
as  loz.  moved  by  the  same  force  freely.  Hence, 
3x64—192  inches,  would  be  the  distance  the  bai 


NATURAL    PHILOSOPTY.  95 

would  fall  freely  in  one  second.  This  distance  is  equal 
to  16  ft.  When  the  experiment  is  accurate,  at  the 
level  of  the  sea,  it  is  found  to  be  16^  ft. 

§  2.   MOTION   PRODUCED  BY   MOKE  THAU   ONE    FORCE. 

(25.)  If  a  body  be  acted  upon  by  two  forces  which, 
separately,  would  cause  it  to  describe  the  adjacent  sides 
of  a  parallelogram,  they  will  be  equivalent  to  a  single 
force,  causing  it  to  move  through  the  diagonal  of  the 
parallelogram. 

Hence  the  effect  of  two  forces  may  be  found  by  rep- 
resenting them  by  the  two  sides  of  a  parallelogram, 
and  then  drawing  the  diagonal. 

1.  If  a  ~body  be   acted  on  oy   two  forces. — Forces 
seldom  act  singly.     It  is  by  the  combined  action  of  at 
least  two,  often  of  more,  that  almost  every  motion  is 
produced.     The  action  of  two  forces  may  be  illustrated 
by  a  very  simple  experiment.     Place  a  ball  at  one 
corner  of  the  table.     Snap  it  with  the  fingers,  length- 
wise of  the  table,  and  it  will  roll  along  the  side ;  or 
snap  it  across  the  table,  and  it  will  roll  across  the  end. 
But  skillfully  snap  it  both  ways  at  the  same  time,  using 
both  hands  for  the  purpose,  and  it  will  roll  in  neither 
of  these  directions,  but  will  move  obliquely  across  the 
table. 

The  same  thing  is  true  of  the  action  of  natural  forces, 
such  as  wind  and  tide.  A  ship,  driven  south  by  a 
direct  wind,  may  at  the  same  time  be  drifted  east  by  a 
tide  moving  eastward.  If  so,  it  will,  at  every  moment, 
be  moving  south  and  east,  or  in  a  straight  line  toward 
the  southeast. 

2.  Actmg  along  the  adjacent  sides  of  a  parallelo- 


96  NATURAL    PHILOSOPHY. 

gram* — The  conditions  of  the  motion  of  both  the  baL 
and  the  ship  may  be  represented  to  the  eye.  Let  A, 
Fig.  33,  represent  the  original  place  of  the  ball  or 
the  ship.  Suppose  that  while  one  force,  if  acting 
alone,  would  move  the  body  to  B,  the  other,  if  acting 
alone,  would  move  it  to  D,  in  the  same  time;  then 
Fig.  83.  when  both  act  at  once,  the  body 

will  neither  go  to  B  nor  D,  but 
will  go  along  the  diagonal  line 
A  C,  and  will  reach  the  point  C  in 
the  same  time  it  would  have  taken 
to  go  to  either  B  or  D. 

3.  They  are  equivalent  to  a  single  force. — The  two 
forces,  acting  in  the  directions  A  B  and  A  D,  produce 
a  single  motion  along  the  line  A  C.     A  single  force 
acting  in  the  direction  of  A  C  would  have  produced  the 
same  effect.     Hence  two  forces,  acting  in  directions  of 
the  sides  of  the  parallelogram,  are  equivalent  to  a  single 
force  acting  in  the  direction  of  the  diagonal. 

The  separate  forces  are  called  components  ;  the  single 
force  which  would  produce  the  same  effect,  is  called  the 
resultant,  and  the  process  of  finding  the  resultant  is 
called  the  composition  of  forces. 

4.  The  resultant  of  forces  may  ~be  found. — The  re- 
sultan  fc  of  two  forces  may  be  found  by  representing 
them  by  two  adjacent  sides  of  a  parallelogram  and 
then    drawing   the    diagonal.      The    lengths    of   the 
lines  represent  the  strength,  or  the  intensity  of  the 
forces. 

In  the  case  of  the  ship,  for  instance:  suppose  the  wind 
able  to  drive  it  10  miles,  while  the  tide  can  drift  it  5 
miles.  To  find  the  actual  path  of  the  ship,  draw  the 
line  A  B,  Fig.  33,  to  represent  the  10  miles,  and  then 


NATURAL    PHILOSOPHY.  97 

the  line  A  D,  at  right  angles  to  it,  and  one  h&lf  as  long, 
to  represent  the  5  miles.  Draw  the  lines  B  C  and  C  D, 
to  complete  the  parallelogram,  and  then  draw  the  dia- 
gonal A  C.  This  line  represents  the  resultant  of  the 
two  forces. 

If  more  than  two  forces  act  at  once,  the  resultant  of 
nil  may  be  found  by  repeating  the  process.  Find  the 
i  esultant  of  two  of  them  first ;  then  compare  this  re- 
sultant and  a  third  force ;  this  second  resultant  and  a 
fourth  force ;  and  so  continue  until  all  the  forces  have 
been  used ;  the  last  *  esultant  will  be  the  resultant  of 
all  the  forces. 

(26.)  'Any  force  may  be  resolved  into  two  others, 
which,  acting  together,  would  produce  the  same  effect. 
This  is  done  when  we  wish  to  know  what  part  of  a 
given  force  can  be  made  available  in  a  direction  dif- 
ferent from  that  in  which  it  is  exerted. 

1.  A  force  may  be  resolved. — To  find  the  compo- 
nents of  a  given  force,  we  may  represent  it  by  a  line, 
and  make  this  line  the  diagonal  of  a  parallelogram ; 
the  adjacent  sides  of  this  parallelogram  will  represent 
the  components.     More  than  one  parallelogram  can  be 
drawn  on  the  same  diagonal ;  so  more  than  one  set  of 
components  may  be  found  for  a  single  force. 

The  process  of  finding  the  components  of  a  single 
force,  is  called  the  resolution  of  forces. 

2.  To  find  the  component  which  acts  in  a  given  direc- 
tion.— WTien  a  ball  is  thrown   obliquely  against  the 
floor,  it  acts  upon  it  with  less  force  than  when  thrown 
perpendicularly  against  it.    But  a  part  of  the  force  will 
Btill  be  exerted  perpendicularly  to  the  floor. 

To  illustrate  this  important  point,  let  a  ball  A,  (Fig. 


98 


NATURAL    PHILOSOPHY. 


Fig.  34. 


34),  be  thrown  against  the  floor,  striking  it  at  C.  We 
may  let  the  line  A  C  represent  the  force  with  which 
the  ball  is  thrown.  JSTow  construct  the  parallelogram, 
by  drawing  the  lines  A  B  and  C  D  perpendicular  to 
the  floor,  and  then  A  D  parallel  to  it.  The  lines  A  B 

and  A  D  represent 
the  components  of 
the  force  A  C. 

The  line  A  B  rep- 
resents the  amount 
of  force  exerted 
perpendicularly  to 
the  floor.  To  make 
the  illustration  more 
specific,  we  will  suppose  that,  measuring  the  lines 
A  C  and  A  B,  we  find  the  latter  to  be  f  as  long 
as  the  former ;  if  so,  then  the  force  exerted  perpendicu- 
larly to  the  floor,  will  be  f  of  the  force  with  which  the 
ball  is  thrown. 

To  find  the  component  which  acts  in  any  given  di- 
rection, we  may  represent  the  original  force  by  a  straight 
line,  and  make  it  the  diagonal  of  a  parallelogram,  one 
of  whose  adjacent  sides  is  in  the  direction  given.  This 
side  will  represent  the  force  required. 

(27.)  Two  forces  may  act  upon  different  points  of  a 
body  in  the  same  direction:  their  resultant  will  be 
equal  to  their  sum.  The  point  of  the  body  to  which 
this  resultant  is  applied,  will  be  as  many  times  nearer  to 
the  greater  force  than  the  smaller  one,  as  the  greater 
exceeds  the  smaller  in  intensity. 

The  weight  of  a  body  is  only  the  resultant  of  a  set  of 
parallel  forces  acting  upon  it  in  the  same  direction :  and 


NATURAL    PHILOSOPHY.  99 

what  is  called  the  center  of  gravity,  is  its  point  of  ap- 
plication. 

1.  Two  forces  in  the  same  direction. — When   two 
forces  act  upon  a  body  in  the  same  direction,  they  pro- 
duce the  same  effect  as  a  single  force  equal  to  their 
sum.     If  two  horses,  for  example,  draw  a  carriage,  one 
with  a  force  of  200  Ibs.,  and  the  other  with  a  force  of 
300  Ibs. ,  it  is  clear  that  a  single  horse,  exerting  a  force 
of  500  Ibs.,  would  produce  the  same  effect. 

2.  The  point  of  application. — But  if  a  single  force 
is  to  take  the  place  of  two  others,  and  produce  exactly 
the  same  motion  as  they  would  when  acting  together, 
at  what  point  of  the  body  shall  it  be  applied  ? 

Suppose  the  body  represented  by  A  B  (Fig.  35),  to 
be  acted  upon  by  two  for- 
ces, represented  by  the  lines  ^  3\o  77 
c  and  d,  one  just  half  the  T? 
length  of  the  other,  the  less-  c\ 
er  force  being  25  Ibs.,  the  * 
greater,  50  Ibs.  Then  the 
line  /*,  just  as  long  as  both 
together,  will  represent  the 
resultant,  a  force  of  75  Ibs. 
JN"ow,  if  this  resultant  is  to  move  A  B,  exactly  as  the 
two  components  would,  it  must  be  applied  at  some 
point,  D,  as  many  times  farther  from  A  than  from  B, 
as  the  force  at  A  is  times  less  than  that  at  B.  Since  c 
is  just  half  of  d,  the  distance  A  D  must  be  just  twice 
as  great  as  B  D. 

3.  The  weight  of  a  l>ody. — A  body  falling  freely,  is 
an  example  of  motion  caused  by  the  action  of  parallel 
components       For.  since  the  force  of  gravitation  acts 


100  NATURAL    PHILOSOPHY. 

upon  every  molecule  of  the  body,  we  may  regard  the 
entire  force  as  made  up  of  as  many  separate  forces  as 
there  are  molecules.  The  sum  of  all  these  components 
is  their  resultant,  and  the  value  of  this  resultant  is  the 
weight  of  the  body. 

4.  The  center  of  gravity. — The  point  of  applica- 
tion of  this  resultant,  is  the  center  of  gravity.  The  cen- 
ter of  gravity  is  usually  defined  to  be — that  point  in  a 
"body  which,  if  supported,  the  body  will  rest  in  any  posi- 
tion. One  can  balance  a  book  on  the  tip  of  his  finger : 
the  tip  of  the  finger  must  be  exactly  under  the  center 
of  gravity  of  the  book.  This  point  being  supported, 
the  whole  body  will  rest. 

The  center  of  gravity  is  the  exact  middle  point  of  a 
body  of  uniform  density  ;  it  is  toward  the  heavier  side 
of  one  that  is  not.  (See  Silliman's  Physics,  pp.  39 
to  45.) 

A  vertical  line  drawn  through  the  center  of  gravity 
is  called  the  line  of  direction,  because  it  shows  the  di- 
rection a  body  will  take  when  allowed  to  fall.  That 
a  body  may  stand  upon  a  plane  surface  without  falling, 
the  line  of  direction  must  pass  through  its  base.  One 
body  stands  more  firmly  than  another,  only  because  it  is 
more  difficult  to  throw  its  line  of  direction  beyond  its 
base.  A  load  of  hay  is  easily  overturned,  because,  the 
center  of  gravity  being  high,  the  line  of  direction  may 
be  easily  thrown  outside  the  base.  A  load  of  stone, 
having  no  greater  weight,  stands  firm,  because,  the  cen- 
ter of  gravity  being  low,  the  line  of  direction  can  with 
difficulty  be  thrown  beyond  its  base. 

Animals  instinctively  incline  their  bodies  always  in 
uich  way  as  to  keep  their  center  of  gravity  over  the 
space  between  their  feet.  Especially  is  this  true  of  man. 


NATURAL    PHILOSOPHY. 


A  body  is  tottering  in  proportion  as  it/nas  great  'height 
and  a  narrow  base  ;  but  it  is  the  prerogative  of  man  to 
be  able  to  support  his  commanding  figure,  erect  and 
firm,  under  constant  changes  of  position,  over  the  verj* 
narrow  base  occupied  by  his  feet. 

(28.)  Curved  motion  is  produced  by  the  action  of  at 
least  two  forces,  one  of  which  is  a  constant  force,  the 
other  may  not  be. 

The  motion  of  a  projectile  is  caused  by  the  constant 
force  of  gravitation,  and  the  impulse  by  which  it  is 
thrown. 

1.  Curved   motion.  —  Whoever  watches  the  varied 
and  beautiful  motions  in  nature,  will  find  that  they  all 
take  place  in  curves.     In  the  ripples  of  the  lake  and 
the  billows  of  the  sea,  he  will  see  a  wonderful  variety 
of  curved  motions.     The  winds,  and  the  clouds  they 
carry,  move  in  curves.     Every  swaying  branch  and 
leaf,   and  every  nodding  stalk  of  grass,  moves  in  a 
curve. 

2.  Is  produced  by  at  least  two  forces.  —  The  motion 
of  a  ball  when  fastened  to  the  end  of  a  string   and 
whirled  around  the  hand,  is  an  example  of  curved  mo- 
tion.    It  is  produced  by  the  action  of  two  forces.     The 
impulse  of  the  hand  H  (Fig.  36), 

which  starts  the  ball,  would,  if  it 
could  act  alone,  carry  it  in  a  straight 
line  from  A  toward  B.  But  the 
string  H  A,  held  firmly  by  the 
hand,  is  a  constant  force  which 
pulls  it  away  from  that  path.  The 
resultant  of  these  two  forces  is 
represented  by  the  circumference  A  B  C  D. 


102  NATURA-L    PHILOSOPHY. 

•  3.  One  of  which  is  constant. — In  the  example  just 
given,  the  force  of  the  hand  is  an  impulsive  force  ;  that 
of  the  string  a  constant  force,  and  a  curved  motion  is 
the  result.  Two  impulsive  forces  will  cause  motion  in 
a  straight  line ;  two  equal  constant  forces  will  do  the 
same.  Two  constant  forces  that  are  unequal  will  cause 
a  curved  motion ;  one,  at  least,  of  the  forces  must  be 
constant. 

The  two  forces  which  cause  curved  motion  are  called 
central  forces.  One  of  them  alone,  acting  upon  the 
ball  at  B  (Fig.  36),  would  carry  it  along  the  line  B  F, 
or  if  the  ball  has  reached  C,  would  move  it  toward  X. 
The  influence  of  this  component  is  to  move  the  ball  in 
a  line  which  is  tangent  to  the  circle  in  which  it  re- 
volves. This  force  is  called  the  centrifugal  force.  The 
other  component,  which  prevents  the  ball  from  moving 
in  a  straight  line  from  the  center  of  motion,  is  called 
the  centripetal  force.  A  simple  and  pleasant  experi- 
ment may  be  performed  to  illustrate  the  effect  of  cen- 
trifugal force.  To  the  handle  of  a  small  pail,  filled 
with  water,  tie  a  cord  firmly.  Grasp  the  cord  and 
swing  the  pail,  fearlessly,  in  a  vertical  circle  over  the 
head  ;  the  centrifugal  force  will  overcome  the  force  of 
gravity,  so  that  not  a  drop  of  water  will  fall,  even  when 
the  pail  is  bottom  side  up  over  the  head. 

Circus  riders  incline  their  bodies  toward  the  center 
of  the  ring  around  which  they  ride,  that  the  centrifugal 
force  may  not  throw  them  from  their  horses.  Carriages, 
in  rapid  motion  around  the  corner  of  a  street,  are  some- 
times overturned  by  this  force.  But  the  most  wonder- 
ful examples  of  the  action  of  central  forces,  are  seen  in 
the  majestic  movements  of  the  heavenly  bodies.  Their 
orbits  are  ellipses.  The  impulse  which  drives  the 


NATURAL    PHILOSOPHY. 


103 


Fig.  8T. 


planets  forward  is  the  centrifugal  force,  while  the  cen- 
tripetal force  is  the  attraction  of  the  sun,  which  holds 
them  in  their  orbits.  ^ 

4.  Projectiles. — Any  body  thrown  into  the  air  is  a 
projectile.     The  stone  from  the  hand,  the  ball  from 
the  gun,  and  the  arrow  from  the  bow,  are  familial 
examples  of  projectiles. 

5.  Their   'motion  is   due  to  two  forces.  —  Leaving 
resistance  of  the  air  out  of  account,  the  motion  of  a 
projectile  is  due  to  the  action  of, 

1st.  The  impulse,  which  starts  it  on  its  journey ;  and, 
2d,  the  constant  force  of  gravity. 

Let  us  suppose  a  cannon  ball,  shot  from  the  point  a 
(Fig.  37),  to  go  in  the  direction  a  I.  At  the  end  of  the 
first  second,  the  impulse  giv- 
en by  the  gunpowder  would 
have  thrown  the  ball  to  some 
point,  as  that  marked  I. 
But  gravitation  will,  at  the 
same  time,  be  pulling  the 
ball  toward  the  ground. 

Represent  the  effect   of  this  . & 

force  in  the  first  second  by 
the  line  a  I'.  The  result- 
ant of  these  two  forces  will 
carry  the  ball  to  the  point  e. 
During  the  next  -second,  the 
impulse  acting  upon  the  ball 
at  e,  would  carry  it  to  s,  just 
as  far  as  it  would  in  the  first,  but  gravitation  would, 
in  the  same  time,  move  it  downward  to  d;  the  resultant 
of  these  two  forces  will  carry  the  ball  to  f.  In  the 
third  second,  the  impulse  would  throw  the  ball  from  f 


104  NATURAL    PHILOSOPHY. 

to  m;  but  gravitation  would  pull  it  down  to  n,  theii 
joint  action  would  carry  it  to  g. 

Now,  let  us  remember  that  gravitation  acts,  not  only 
at  the  beginning  of  each  second,  as  the  figure  repre 
sents  it,  but  also  at  every  other  instant^  so  that  the  path 
of  the  ball  will  bend,  not  at  the  points  #,/*,  and  g  alone, 
but  at  every  point  between  these,  thus  forming  a  curve 
reaching  the  ground  at  h. 

The  horizontal  distance,  a  A,  is  called  the  range  or 
the  random  of  the  projectile. 

This  distance  depends  upon  the  force  applied  to  the 
projectile,  and  the  angle  at  which  it  is  thrown.  Theory 
requires  that  the  random  be  greatest  when  the  pro- 
jectile is  thrown  at  an  angle  of  45° ;  but  the  resistance 
of  the  air  very  much  modifies  the  motion,  so  that,  in 
practice,  the  greatest  range  is  obtained  at  an  angle 
much  below  45°.  The  greatest  range  of  an  arrow  is 
when  the  angle  is  about  36°. 

The  science  of  gunnery  rests  upon  the  laws  of  pro- 
jectiles. The  most  skillful  gunner  is  he  who  can  most 
accurately,  under  all  circumstances,  compare  and  com- 
bine the  forces  of  gunpowder,  gravitation,  and  the 
resistance  of  the  air. 

§  3.    THE   INDESTRUCTIBILITY    OF   FORCE. 

(29.)  Force,  like  matter,  is  indestructible.  What- 
ever force  has  acted  to  put  a  body  in  motion,  the  same 
amount  must  be  exerted  by  the  moving  body  npoc 
others,  before  it  can  come  to  rest. 

Three  well-marked  cases  are  before  us : — 
1st.  In  which  a  body  moves  without  resistance  from 
other  bodies; 


JSATURAL    PHILOSOPHY.  1Q5 

2d.  In  which  a  body,  moved  by  an  impulsive  force, 
meets  with  resistance ; 

3d.  In  which  a  constant  force  is  applied  to  overcome 
the  resistance. 

1.  Force  is  indestructible. — It  was  once  thought  that 
bodies  of  matter  could  be  destroyed.    It  seems  so  yet 
to  a  careless  observer  ;  but  when  he  has  learned  how 
to  search  for  their  scattered  fragments,  he  finds  that 
every  atom  still  exists.     Forces  likewise  vanish;  but 
when  the  motions  they  produce  have  been  changed  to 
rest,  and  after  every  trace  of  their  action  seems  to  have 
been  lost,  they  have  been  chased  from  their  hiding- 
places,  until  it  is  proved  that  every  impulse  still  acts — 
that  while  it  may  change  from  form  to  form,  and  show 
itself  in  a  multitude  of  ways,  yet  .not  a  single  impulse 
of  force  can  be  destroyed. 

2.  Motion  can  not  cease  without  exerting  the  same 
amount   of  force  which  produced  it. — The  force  of 
gunpowder  is  expended  in  giving  motion  to  a  ball :  the 
ball  exerts  the  same  force  upon  whatever  obstacles  it 
meets.     A  small  force  will  give  slow  motion ;  the  body 
moving  slowly,  will,  on  meeting  an  obstacle,  exert  the 
same  small  force.     A  greater  force  will  give  a  swifter 
motion ;  the  body  moving  swiftly  will  strike  another 
with  the  same  greater  force.    Thus  a  bullet  may  simply 
bruise  an  arm,  or  it  may  pierce  a  tree,  or  shatter  a 
block  of  the  hardest  stone,  according  to  the  velocity 
with  which  it  strikes ;  and  the  velocity  will,  in  turn, 
depend  upon   the  force  which   puts  the  ball  in   mo- 
tion. 

3.  Suppose   a    l)ody   move    without    resistance. — If 
a  body  should  move  without  any  resistance   to    ita 

6* 


106  NATURAL    PHILOSOPHY. 

motion,  until  it  suddenly  strikes  an  obstacle,  the  force 
with  which  it  would  strike,  would  be  exactly  equal  to 
that  which  gave  it  motion.  If  a  force  of  ten  pounds 
puts  a  body  in  motion,  it  would  hit  the  other  with  a 
ten -pound  force.  The  force  which  a  body  moving 
without  resistance  can  exert  upon  an  obstacle  is  called 
its  momentum. 

Suppose  a  body,  weighing  1  lb.,  move  with  a  velocity 
of  1  ft.  a  second.  If  it  meet  with  no  resistance,  it  will 
strike  another  body  with  a  certain  force,  or  momentum, 
which  we  will  call  1.  The  momentum  of  a  2  lb.  weight, 
with  the  same*  velocity,  would  be  twice  as  great ;  it 
would  be  2.  A  weight  of  1  lb.  moving  twice  as  fast, 
would  also  have  twice  the  momentum  of  the  first ;  it 
would  be  2.  A  weight  of  3  Ibs.,  would  have  a  momen- 
tum of  3,  and  then,  if  its  velocity  be  doubled,  it  would, 
on  that  account,  have  twice  as  much  momentum ;  it 
would  be  6.  The  momentum  of  a  moving  body  is  thus 
seen  to  vary  with  its  weight  and  its  velocity,  and  we 
find  that  the  momentum  of  a  ~body  is  equal  to  the  prod- 
uct of  its  weight  multiplied  by  its  velocity. 

4.  /Suppose  motion  due  to  an  impulse  meet  with  resist- 
ances.— When  a  moving  body  meets  with  the  resistance 
of  air,  of  friction,  or  of  any  other  influence,  before  it 
strikes  another,  the  force  which  started  it  will  be  ex- 
erted, partly  upon  this  resistance,  and  partly  upon 
the  object  which  it  finally  strikes ;  but  the  sum  of  these 
two  parts  will  exactly  equal  the  force  which  set  the 
body  moving.  Thus  a  stone  thrown  from  the  hand  will 
strike  a  tree  at  a  distance  with  much  less  force  than  it 
leceives,  but  in  its  motion  it  has  been  compelled  to 
move  the  air  before  it,  and  if  the  force  which  it  exerts 
in  this  way,  be  added  to  that  which  it  exerts  on  the 


NATURAL    PHILOSOPHY.  1QT 

tree,  the  aggiegate  will  be  just  equal  to  that  which  the 
hand  exerted  upon  the  stone  at  first. 

So,  if  a  ball  be  rolled  upon  the  ground,  its  force  must 
act  upon  the  air  in  front  of  it,  and  upon  the  roughness 
of  the  ground  under  it :  all  its  force  is  thus  used,  and  it 
stops;  but  the  total  amount  gradually  expended  in 
this  way,  must  just  equal  the  sudden  impulse  which 
started  the  ball  upon  its  journey. 

5.  Suppose  a  constant  force  applied  to  overcome  re- 
sistances.— When  a  constant  force  is  applied  to  keep 
the  body  moving  uniformly,  in  spite  of  resistances,  the 
force  with  which  it  strikes  an  obstacle  must  be  equal  to 
that  which  acts  to  keep  it  moving.  Thus,  if  a  train  of 
cars,  kept  in  motion  at  the  rate  of  20  miles  an  hour, 
suddenly  strike  another  train  going  with  equal  velocity 
in  the  opposite  direction,  the  entire  force  of  steam, 
expended  to  keep  up  the  motion  of  both  trains,  will  be 
suddenly  exerted  to  dash  them  both  to  pieces. 

This  force,  which  a  body,  moving  against  resistances 
with  a  uniform  motion  kept  up  by  a  constant  force,  will 
exert  upon  an  obstacle,  is  called  living  force,  or  vis 
viva. 

Now,  if  the  velocity  of  a  body  be  doubled,  the  force 
required  to  keep  it  uniform  will  be  four  times  as  great. 
Take  the  case  of  a  ship  moving  through  water.  If  the 
velocity  of  the  ship  be  doubled,  twice  as  much  water 
will  have  to  be  moved  in  the  same  time  ;  it  will  take  a 
double  force  to  do  this.  Moreover,  every  particle  of 
water  will  have  to  be  moved  twice  as  fast ;  it  will  take 
a  double  force  to  do  this  also.  To  do  both  these  things 
at  the  same  time,  the  force  must  be  twice  doubled, 
or  made  four  times  as  great.  This  is  true  of  all  resist- 
ances, and  for  all  velocities.  In  other  words,  the  forco 


108  NATURAL    PHILOSOPHY. 

required  to  keep  a  body  moving  against  resistances, 
will  be  in  proportion  to  the  square  of  the  velocity. 

But  when,  under  such  circumstances,  the  moving 
body  strikes  an  obstacle,  the  force  which  keeps  it  mov- 
ing, must  be  suddenly  exerted  upon  the  body  struck. 
It  thus  appears  that  the  living  force  of  a  body  is  in 
proportion  to  the  square  of  its  velocity.  It  is  equal 
to  the  product  of  the  weight  multiplied  by  the  square 
of  the  velocity. 

§   4.   OF  MACHINERY. 

(30.)  The  principle  of  momentum  applied  to  any- 
one of  the  simple  machines,  will  determine  its  law  of 
equilibrium. 

1.  The  principle  of  'momentum. — Momentum  has 
been  defined  to  be  the  force  which  a  moving  body, 
meeting  no  resistances,  can  exert.  Now,  two  bodies 
exerting  equal  forces  upon  each  other  in  opposite  direc- 
tions, will,  when  at  rest,  just  balance  each  other,  or  be 
in  equilibrium.  This  principle  is  called  the  principle 
of  momentum.  It  states  briefly  that  two  forces,  in 
opposite  directions,  will  be  in  equilibrium  when  their 
momenta  are  equal. 

Let  us  illustrate  a  single  case  by  means  of  Fig.  38. 
Fig.  38.  Suppose  two  bodies,  M  and 

-2- • ^   N,  hang  from  the  ends  of  a 

A  bar,  A  B,  which  rests  upon 

I  the  point  C,  about  which  it 
y  ®  may  freely  turn.  If  it  does 
turn,  and  M  goes  up,  N  will  go  dowr,  and  if  the  dis- 
tance B  C  is  twice  the  distance  A  C,  then  "N  will  go  twice 
as  fast  as  M.  In  all  cases,  the  velocities  of  the  two 


NATURAL    PHILOSOPHY.  1Q9 

bodies  will  have  the  same  ratio  as  their  distances^  A  B 
and  B  0,  from  the  center  of  motion.  These  lines  may 
then  l)e  taken  to  represent  velocities.  Then  the  mo- 
mentum of  M  will  be  M  x  A  C,  and  that  of  N  will  be 
N  x  B  C.  Now  if  these  momenta  are  equal,  then  the 
two  bodies  will  be  exerting  equal  forces  upon  the  bar 
A  B,  and  if  once  brought  to  rest,  they  will  just  balance 
each  other. 

2.  Machines. — Machines  are  instruments  by  which 
forces  may  be  applied  to  overcome  resistance,  or  do 
work.    They  are  so. made  that  a  small  force,  by  moving 
rapidly,  may  overcome  a  greater  resistance,  or  a  great 
force,  by  moving  slowly,  may  put  a  small  resistance  in 
rapid  motion.     In  all  cases  the  momenta  of  the  two 
forces  must  be  equal. 

The  resistance  to  be  overcome  is  always  called  the 
weight:  the  force  which  overcomes  it  is  called  the 
power. 

3.  Simple  machines. — There  are  six  simple  forms  of 
machines,  usually  called  the  mechanical  powers.     Out 
of  these  six  simple  machines  all  forms  of  machinery, 
complex  as  they  may  be,  are  made.    We  name  them  in 
the  order  which  is  to  be  followed  in  describing  them. 

1.  The  Lever.  4.  The  Inclined  Plane. 

2.  The  Wheel  and  Axle.       5.  The  Wedge. 

3.  The  Pulley.  6.  The  Screw. 

4.  The  law  of  equilibrium. — By  the  term,  law  of 
equilibrium,  is  meant  a  statement  of  the  relation  which 
must  exist  between  the  power  and  the  weight,  in  order 
that,  when  at  rest,  they  may  just  balance  each  other. 

.  (31.)  Levers   are  of  three   classes.      The   principle 
of  momentum  applied  to  the  lever,  shows  that  the  power 


,110  NATURAL    PHILOSOPHY. 

and  weight  will  be  in  equilibrium  when  they  are  to  each 

Fig.  sa  other  inversely   as   the 

B  F       A  perpendicular  distances 

* from  the  fulcrum  to  the 

directions  in  which  they 

act.      A  compound  lever  acts  on  the  same  principle. 
Applications  of  the  lever  are  very  numerous. 

1.  Levers. — A  lever  is  an  inflexible  bar,  able  to  turn 
freely  upon  one  point.    Thus,  if  the  line  A  B  (Fig.  39) 
represents  an  inflexible  bar,  resting  upon  some  support 
at  F,  upon  which  FJ£.  40. 

it  has  free  motion,   ^ F  p 

it  represents  a 
lever.  The  point 
F,  about  which 
the  lever  turns, 
is  called  t*h&  fulcrum. 

2.  Three  classes  of  levers. — That  point  of  a  lever  to 

F1«-  4t  which  the  power  is 

applied,  is  called 
the  point  of  appli- 
cation. That  on 
which  the  weight 
acts  is  called  the 
working  point. 
Now,  the  lever 
takes  different 
names  according  to 
the  relative  posi- 
tions of  the  point  of  application,  the  working  point, 
and  the  fulcrum.  In  the  lever  represented  in  Fig.  40, 
whose  fulcrum  is  at  F,  a  power  (P)  acts  upon  ono 


NATURAL    PHILOSOPHY. 


Ill 


end  of  the  lever  (A)  while  a  weight  (W)  acts   upon 
the  other  (B).     The  fulcrum  is  between  the  point  of 


Fig.  42. 


Fig.  48. 


application  and  the  working  point.     This  is  called  a 
lever  of  ther^  class. 


Fig.  44. 


In  the  lever,  Fig.  41,  the  working  point  B,  is  be- 
tween the  point  of  application  A,  and  the  fulcrum  E, 
This  is  a  lever  of  the  second  class. 


112  NATURAL    PHILOSOPHY. 

In  the  lever,  Fig.  42,  the  point  of  application  (A)  ia 
between  the  working  point  (B)  and  the  fulcrum,  F. 
This  is  a  lever  of  the  third  class. 

All  levers  belong  to  these  three  classes.  They  need 
not,  however,  be  made  in  the  simple  straight  form  shown 
by  the  figures.  In  Fig.  43,  the  line  A  F  B  represents 
a  lever  whose  arms  make  a  right  angle  at  the  fulcrum, 
F.  It  is  a  lever  of  the  first  class ;  so  also  is  that  shown 
in  Fig.  44,  by  the  curved  line  A  F  B. 

3.  Application  of  the  principle  of  momenta. — Now 
if  we  examine  the  figures  which  represent  the  three 
classes  of  lever,  we  see  that  in  each  one,  the  power  (P) 
and  the  weight  (W)  are  two  forces  which  act  in  opposite 
directions.  They  will  be  able  to  just  balance  each 
.other,  when  of  such  strength  that,  when  moving,  their 
momenta  are  equal.  The  lines  B  F  and  A  F  represent 
their  velocities  [see  (30.)  1].  The  momentum  of  the 
power  is  therefore  P  x  A  F;  that  of  the  weight  is  W  x  B  F. 
If  equilibrium  takes  place  only  when  the  momenta  are 
equal,  then 

PxAF  =WxBF;  hence, 
P  :  W  :  :  B  F  :  A  F. 

This  proportion  teaches  us  that  the  power  and  weight 
will  be  in  equilibrium,  when  they  are  to  each  other  in- 
verpely  as  the  distance  of  their  points  of  application 
from  the  fulcrum. 

It  may  be,  however,  that  the  power  and  weight  do 
not  act  perpendicularly  upon  the  lever.  This  case  is 
represented  by  Fig.  44.  The  lever  A  B  has  its  ful- 
crum at  F.  The  power  (P)  and  the  weight  (W)  act 
obliquely  at  B  and  A.  Now  it  is  evident  that  tha 
force  of  the  power,  acting  obliquely  at  B,  is  not  all  ex- 
pended to  lower  the  lever  [see  (26.)  2],  but  that  it'  it 


NATURAL    PHILOSOPHY.  U3 

were  acting  upon  the  point  N,  perpendicularly,  it  would 
exert  all  its  force  to  move  the  arm  N  F.     So  the  effect 
of  the   weight  acting  obliquely  upon  A,  will  be  the 
same  as  if  it  were  acting  perpendicularly  upon  an  arm, 
M  F.    Hence,  P  x  N  F  may  be  taken  as  the  momentum 
of  the  power,  and  W  x  M  F  as  the  momentum  of  the 
weight.     Putting  these  momenta  equal, 
PxN  F=WxMF;  hence, 
JP  :  W  :  :  M  F  :  N  F. 

This  proportion  teaches  that  the  power  and  weight 
will  be  in  equilibrium,  when  the  power  and  weight  are 
inversely  as  the  perpendicular  distances  from  the  ful- 
crum to  the  directions  in  which  they  act. 

Thia  principle  is  called  the  law  of  equilibrium  for 
the  lever.  It  will  apply  to  all  possible  forms. 

4.  The  compound  lever. — In  a  compound  lever 
several  simple  levers  are  generally  so  fixed,  that  the 
short  arm  of  one  may  act  upon  the  long  arm  of  another. 
Fig.  45  shows  a  compound  Fig.  48. 

lever  made  up  of  two  simple 
levers  having  their  fulcrums 
at  F,  and  F7. 

In  this  case  the  momentum 
of  the  power  will  be  equal  to 
PxC  FxBF',  and  that  of 
the  weight  will  be  equal  to  W  x  D  F'  x  A  F.  If  these 
products  are  put  into  the  form  of  an  equation  it  will  be 
seen  that  the  power  and  weight  will  be  in  equilibrium 
when  the  power  multiplied  by  the  product  of  all  the 
arms  on  its  side  of  the  fulcrum,  is  equal  to  the  weight 
multiplied  by  the  product  of  all  the  arms  on  its  side. 

The  compound  lever  is  used  when  a  small  force  is 
required  to  sustain  a  large  weight,  and  it  is  not  conve- 


114 


NATURAL    PHILOSOPHY. 


Fig.  46. 


nient  to  have  a  very  long  lever.  If  the  long  arms  of 
the  simple  lever  be  6  and  8  ft.,  and  each  short  arm  is 
1  ft.,  then  1  Ib.  power  at  0,  will  balance  48  Ibs.  at  D ; 
while  if  a  simple  lever  had  been  used  whose  long  arm 
was  as  long  as  those  two  long  ones  together,  6  +  8=14  ft., 
and  whose  short  arm  was  1  ft.,  then  1  Ib.  at  C,  would 
only  be  enough  to  balance  14  Ibs.  at  D. 

5.  Applications  of  tJw  lever. — Of  levers  of  the  first 
kind  many  familiar  examples  might  be  named.  The 
handspike  and  crow-bar  are  levers  of  this  class.  Shears 
and  pincers  are  pairs  of  levers,  also  of  the  first  class ; 
their  fulcrums  being  at  their  joints. 

The  balance  is  one  of  the  most  useful  applications 
of  the  lever.  Fig.  46  represents  this  instrument. 

The  beam  a  b  is  a  lever 
poised  at-  its  centre,  the 
pivot  or  fulcrum  c  being  a 
little  above  its  center  of  grav- 
ity. From  the  ends  of  the 
beam  the  scale  pans  are 
hung,  in  one  of  which  is  put 
the  body  to  be  weighed,  and  in  the  other,  the  weights 
of  metal  to  balance  it.  Balances  are  of  continual  use 
in  commerce ;  they  are  indispensable  in  the  laboratory 
of  the  chemist,  for  whose  use 
they  are  made  with  so  great, 
skill  that  a  weight  equal  to 
the  10,000  of  a  grain  can  be 
easily  weighed. 

The  steelyard  is  also  a  lever 
of  the  first  class,  but  with  un- 
equal   arms.      The  body   W, 
Fig.  47,  to  be  weighed,  is  hung  from  the  short  arm  of 


NATURAL    PHILOSOPHY.  ^5 

the  lever  S  B,  and  it  is  balanced  by  a  small  weight, 
P.  It  is  clear  that  this  small  weight  will  balance  more 
weight  in  the  body  W,  as  it  is  moved  farther  and 
farther  from  the  fulcrum  C.  The  arm  B  C  has  notches 
cut  upon  it,  and  numbered,  to  denote  the  pounds  or 
ounces  in  "W,  balanced  by  P,  when  at  these  points. 

Levers  of  the  second  class  are  not  so  common ;  the 
wheelbarrow,  however,  is  an  example  sufficiently  fa- 
miliar. The  axle  of  the  wheel  is  the  fulcrum,  to  the 
opposite  ends  of  the  handles  the  power  is  applied,  while 
the  load,  or  the  weight,  rests  between  these  points. 
The  oar  of  a  boat  is  a  lever  of  this  kind,  where,  singu- 
larly enough,  the  unstable  water  serves  as  a  fulcrum ; 
the  hand  is  the  power  at  the  other  end  of  the  lever, 
while  the  boat  is  the  weight  between  them. 

Levers  of  the  third  class  are  often  met  with  in  the 
arts.  The  common  fire-tongs  and  the  sheep-shears  are 
pairs  of  levers  of  this  kind.  Their  fulcrums  are  at  one 
end ;  the  resistance  to  be  overcome  is  put  between 
their  parts  near  the  other  end,  while  the  fingers,  which 
afford  the  power,  are  between  the  fulcrum  and  the 
weight. 

(32.)  The  wheel  and  axle  acts  on  the  principle  of  a 
lever.  The  power  and  weight  will  be  in  equilibrium 
when  the  power  is  to  the  weight  as  the  radius  of  the 
axle  is  to  the  radius  of  the  wheel. 

A  compound  wheel  and  axle  acts  on  the  same  prin- 
ciple as  a  compound  lever. 

One  wheel  may  be  made  to  turn  another  by  friction, 
by  cogs,  or  by  bands. 

Applications  of  this  machine  are  common  and  im- 
portant. 


116 


NATURAL    PHILOSOPHY. 


1.  The  wheel  and  axle. — One  form  of  the  wheel 
axle  is  shown  in  Fig.  48.     It  consists  of  a  wheel  (B) 
firmly  fastened  to  an  axle  (A),  and  turning  freely  around 
an  axis,  one  end  of  which  is  shown  at  C.     The  power 
(P)  acts  upon  the  circumference  of  the  wheel,  and  the 
weight  (W)  acts  upon  the  axle  by  means  of  \  rope 
winding  around  it  in  the  opposite  direction. 

2.  It  acts  on   the  principle  of  tke    lever.  — If  we 
have  an  end  view  of  the  machine,  it  will  be  seen,  as 
shown  in  Fig.  49,  where  the  large  circle  represents  the 
wheel,  and  the  small  circle,  the  axle ;    the  center  0, 
being  the  end  of  the  axis.     At  the  point  A,  the  power 

Fig.  49 


acts  on  the  wheel,  and  from  the  point  B,  on  the  other 
side  of  the  center,  the  weight  is  suspended.  Now, 
if  a  straight  line  A  B  join  the  points  A  and  B,  it  will 
pass  through  the  center,  and  represent  a  lever,  whose 
fulcrum  is  at  0.  It  is  upon  the  ends  of  such  a  lever 
that  the  power  and  weight  are  constantly  acting. 

3  Application  of  the  principles  of  momentum. — 
The  momentum  of  the  power  is  P  x  A  C ;   that  of  the 
weight  is  W  x  B  C.   If  the  two  forces  are  able  to  bal- 
ance each  other,  these  momenta  are  equal.     Hence, 
PxAC=WxBC:  or, 
P  :  W  :  :  B  0  :  AC. 


NATURAL    PHILOSOPHY.  H7 

But,  in  the  figure,  we  notice  that  A  C  is  the  radius 
of  the  wheel,  and  that  B  C  is  the  radius  of  the  axle, 
Then  the  proportion  teaches  us  that  the  power  cmd 
weight  will  be  in  equilibrium  when  the  power  is  to  the 
weight,  as  the  radius  of  the  axle  is  to  the  radius  of  the 
wheel. 

If  the  radius  of  the  axle  is  1  ft,  and  that  of  the  wheel 
3  ft.,  then  1  lb.  will  balance  3  Ibs. 

4.  The  compound  wheel  and  axle. — When  more  than 
one  wheel  and  axle  are  connected,  so  that  the  axle  of 
each  may  act  on  the  wheel  of  the  next,  the  machine  is 
a  compound  wheel  and  axle.  Such  an  arrangement  is 
shown  in  Fig.  50.  We  may  get  the  law  of  equilibrium 
in  the  same  way  as  in  the  '  Fig  50 

compound  lever.  The  mo- 
mentum of  the  power  will 
be  P,  multiplied  by  the  sev- 
eral radii  of  the  wheels ;  that 
of  the  weight  will  be  W, 
multiplied  by  the  several 
radii  of  the  axles.  If  the 
two  forces  are  able  to  balance 
each  other,  these  values  must 
be  equal.  Hence  we  learn, 
that  in  a  compound  wheel 

and  axle,  the  power  and  weight  will  be  in  equilibrium, 
when  the  power  multiplied  by  the  product  of  the  radii 
of  the  wheels,  equals  the  weight  multiplied  by  the  pro- 
duct of  the  radii  of  the  axles. 

It  is  easy  to  see  that,  in  this  way,  a  small  power  may 
be  made  to  balance  a  much  larger  weight  than  it  could 
by  acting  upon  a  simple  wheel  and  axle,  unless  the 
wheel  should  be  so  large  as  to  be  unwieldy. 


118  NATURAL    PHILOSOPHY. 

5.  One  wheel  may  turn  another  by  means  of  cogs.— 
In  Fig.  50,  there  may  be  seen  projecting  teeth  on  the 
circumferences  of  the  axles,  ~b  and  c,  which  fit  into  equal 
notches  on  the  circumferences  of  the  wheels.      Neither 
the  axles  nor  the  wheels  can  turn  without  causing  the 
other  to  turn  also.     This  is  the  common  and  conve- 
nient method  of  giving  motion  from  one  wheel  to  an- 
other.    The  wheels  of  a  clock  are  cog-wheels :   those  of 
a  watch  also  beautifully  illustrate  this  mode  of  commu- 
nicating motion. 

6.  By  friction. — When  the  circumferences  of  the 
wheels  and  the  axles  are  made   smooth,  they  may  be 
pressed  so  snugly  together,  that  neither  can  turn  with- 
out turning  the  other  at  the  same  time,  in  the  opposite 
direction.     In  this  case,  the  motion  is  communicated  by 
the  friction  of  the  parts  against  each  other. 

7.  By  bands — A  third  method  of  giving  motion  to  a 
train  of  wheel- work,  consists  in  the  use  of  bands  or 
belts,  which  encircle  the  parts  which  are  to  act  upon  each 
other.     In  the  spinning-wheel,  for  example,  the  spindle 
is  turned  by  a  band  which  passes  around  it  and  the  axle 
of  the  wheel-head.    Another  band  passes  around  the 
wheel-head  and  the  large  wheel,  which  is  turned  by  the 
hand   of  the   spinner.      From  the  horse-power   of  a 
thrashing-machine,  also,  motion  is  given  to  the  cylin 
der  by  means  of  a  belt. 

8.  Applications  of  the  wheel  and  axle. — Many  forms 
of  the  wheel  and  axle  are  in  common  use :  the  windlass 
is  one  of  the  most  familiar,  being  often  used  to  raise 
water  from  wells.     One  form  of  the  windlass  is  repre- 
sented in  Fig.  48.   A  cra«ik  is  often  used  in  place  of  the 
wheel,  B.      The  common  grindstone  is  a  homely  illus- 
tration of  the  wheel  and  axle :  the  crank  is  in  place  of 


NATUEAL    PHILOSOPHY.  ll£ 

b  wheJ  ;  the  stone  itself  is  the  axle.  The  power  is  the 
force  of  the  hand,  while  the  weight  is  the  resistance  of 
fered  by  the  tool  pressing  on  the  edge  of  the  stone. 

If  the  axle  is  in  a  vertical  position,  and  the  forces  of 
power  and  weight  act  horizontally,  the  machine  is  then 
called  a  capstan,  and  is  much  used  on  board  of  ships. 

The  compound  wheel  and  axle  is  used  in  almost  ev- 
ery mill  and  factory.  Two  objects  are  sought  in  ita 
use :  either  great  resistance  is  to  be  overcome,  or  rapid 
motion  is  to  be  secured.  To  overcome  great  resistances, 
the  power  is  applied  to  the  circumference  of  the  first 
wheel  in  the  system,  and  the  weight  is  acted  upon  by 
the  last  axle.  This  case  is  shown  in  Fig.  50.  To  secure 
rapid  motion,  the  power  is  applied  to  the  first  axle, 
while  the  weight  is  acted  upon  by  the  circumference  of 
the  last  wheel.  The  same  figure  illustrates  this  case 
also,  if  we  will  suppose  the  heavy  body  W,  to  act  as  a 
power  to  put  the  lighter  body  P,  in  motion.  If  we 
suppose  the  radius  of  each  axle  to  be  1  ft.,  and  of  each 
wheel  10  ft,  then  P  xlO  xlO  xlO=Wx  1  xl  x  1 :  or, 
1,000  P="W".  Now,  W  being  1,000  times  heavier  than 
P,  P  must  move  1,000  times  faster  than  W.  In  this 
way,  a  great  power  may  be  changed  into  rapid  motion. 
An  example  of  this  is  found  in  the  saw-mill  where  the 
slow  motion  of  a  heavy  body  of  water,  acting  against 
a  water-wheel,  is  given,  by  means  of  cogs  and  belts, 
from  wheel  to  wheel,  until  it  reappears,  multiplied  a 
thousandfold,  in  the  buzzing  saw.  ^ 

(33.)  The  pulley  may  be  either  fixed  or  movable. 
In  the  fixed  pulley  the  power  and  weight  will  be  in 
equilibrium  when  they  are  equal. 

In  the   movable    pulley,  with   a   single  rope,   the 


120 


NATURAL    PHILOSOIHY. 


power  and  weight  will  be  in  equilibrium  when  the 
power  is  equal  to  the  weight,  divided  by  the  number 
of  branches  of  rope  which  sustains  the  weight. 

In  movable  pulleys,  with  separate  ropes,  the  power 
and  weight  will  be  in  equilibrium  when  the  power 
equals  the  weight,  divided  by  2,  raised  to  a  power, 
shown  by  the  number  of  pulleys. 

The  applications  of  the  pulley  are  common  and  im- 
portant. 

1.  The  pulley. — A  pulley  is  a  grooved  wheel,  turning 
freely  about  its  axis,  with  a  rope  passing  over  or 
around  it.  It  is  shown  in  Fig.  51.  The  grooved 

Fig.  51.  Fig.  52. 

B  03 


whee.  A,  moves  freely  upon  its  axis,  while  over  its 
circumference  goes  the  rope,  to  the  ends  of  which  the 
power  and  the  weight  are  fastened. 

2.  Is  either  fixed  or  movable. — If  the  axis  of  the 
pulley  is  stationary  (see  Fig.  51),  the  pulley  is  called  a 


NATURAL    PHILOSOPHY,  121 

•fixed  pulley.  The  movable  pulley  is  one  whose  axis 
moves  with  the  weight.  This  will  be  understood  by 
means  of  Fig.  52.  The  wheel  E,  is  a  movable  pulley. 
From  its  axis  the  weight  is  hung,  while  the  rope,  one 
end  of  which  is  fastened  to  a  fixed  support  at  D,  passes 
under  it  and  then  over  a  fixed  pulley  A.  The  power 
is  applied  to  this  end  of  the  rope. 

3.  The  principle  of  momentum  applied  to  the  fixed 
pulley. — The   fixed   pulley   is  shown   in   Fig.   51,   to 
which  we  again  refer.     It  is  clear  that,  when  motion 
occurs,  the  power  (P)  will  go  down  with  exactly  the 
same  velocity  as   the  weight  (W)  goes  up.     To  have 
equal  momenta    when    the  velocities    are   equal,   the 
bodies  must  have  equal  weights.      Hence,  in  the  fixed 
pulley  the  power  and  weight  can  balance  each  other  only 
when  they  are  equal. 

4.  The  principle  of  momentum  applied       Fig.  53. 
io  the  movable  pulley  with  a  single  rope. — 

In  the  movable  pulley,  with  a  single  rope 
(see  Fig.  52),  the  weight  rests  upon  two 
branches  of  the  rope,  H  and  E,  and  when 
it  rises,  both  branches  must  be  equally 
shortened.  But  the  rope  F  P  will  lengthen 
just  as  much  as  both  the  branches  shorten. 
The  power  (P)  moves  downward  just  twice 
as  fast  as  the  weight  (W)  goes  up.  Let  V 
represent  the  velocity  of  the  power,  then  J 
will  represent  the  velocity  of  the  weight, 
The  momentum  of  P  will  be  P  x  Y,  and 
that  of  W  will  be  WxJ,  and  the  two 
forces  can  balance  when 

P  x  Y= W  x  J,  or,  when  P=^. 
Now  let  us  take  another  case.     Suppose  there  are 


122 


NATURAL    PHILOSOPHY. 


two  movable  pulleys,  C  and  D  (Fig.  53),  with  a  single 
rope,  one  end  being  fastened  at  F,  while  to  the  other 
end  the  power  P,  is  applied.  In  this  case  we  find  that 
the  weight  is  supported  by  four  branches  of  the  rope, 
and  we  see,  too,  that  when  it  rises,  all  four  of  these 
branches  must  be  shortened  alike.  But  the  rope,  E  P, 
rnu^t  at  the  same  time  lengthen  as  much  as  all  the 
branches  shorten,  so  that  the  velocity  of  P  downward 
must  be  four  times  as  great  as  that  of  W  upward. 
Then,  if  V  is  the  velocity  of  P,  J  will  be  the  velocity 
of  W ;  and,  if  their  momenta  are  equal, 
PxV=WxJ,  or,P=J. 

In  like  manner,  if  three  movable  pulleys  are  used, 
we  should  find  that,  to  be  in  equilibrium,  P=^. 

If,  now,  we  notice  that  in  each  of  the  values  of  P 
just  found,  the  denominator  of  the  fraction  is  the  num- 
ber of  branches  of  the  rope  which  supports  the  weight, 
rig.  54.          we   have    this   general   principle :    in 
movable  pulleys,  with  a  single  rope,  the 
power  and  weight  will  be  in  equilibrium 
when' the  power  equals  the  weight  di- 
vided by  the  number  of  branches  which 
support  it. 

5.  The  movable  pulley  with  sepa- 
rate ropes. — When  each  pulley  has  a 
separate  rope,  the  law  is  very  different. 
Fig.  54:  shows  such  a  system.  The 
three  ropes,  a  b  0,  are  fastened  to  the 
beam  H  K.  The  first,  after  passing 
around  the  pulley  A,  is  fastened  to  the 
axis  of  the  one  above:  so  the  rope  5,  after  going 
around  the  pulley  B,  is  fastened  to  the  axis  of  C :  but 
the  rope  c,  after  going  over  the  pulley  C,  passes  over 


NATURAL    PHILOSOPHT.  123 

a  fixed  pulley,  and  receives  the  power  at  the  other 
end. 

6.  The  principle  of  momentum  applied  to  the  mov 
able  pulley  with  separate  ropes. — This  system  is  onlj 
a  combination  of  movable  pulleys  with  a  single  rope. 
Suppose  the  pulleys  A  and  B  were  taken  away,  the 
weight  being  hung  from  the  axis  of  C,  there  would  be 
left  an  arrangement  exactly  like  that  shown  in  Fig.  52, 
C  is  a  movable  pulley,  with  a  single  rope,  to  lift  the  pul 
ley  B.     B  is  likewise  a  movable  pulley,  with  a  single 
rope,  to  lift  the  pulley  A  ;  while  A  is  itself  a  movable 
pulley,  with  a  single  rope,  to  lift  the  weight  W.   No  new 
application   of  momentum  is  needed.     The  effect  of 
the  power  (P)  will  be  doubled  by  each  pulley  thus : — 

With  1  pulley,    P=y=J; 
«     2  pulleys,  P  =^=5; 

«      3        «        P-^-^ 

~  8  "  23' 

If  we  notice  that  the  denominator  in  each  of  thescj 
values  of  P,  is  a  power  of  2,  whose  index  is  the  num- 
ber of  pulleys,  we  infer  that,  in  a  system  of  movable  pul 
leys  with  separate  ropes,  the  power  and  weight  will  be  in 
equilibrium  when  the  power  equals  the  weight  divided 
by  a  power  of  2,  whose  index  is  the  number  of  pulleys. 

For  example,  with  a  system  of  5  pulleys,  how  much 
weight  will  a  power  of  10  Ibs.  balance  \ 

P  -=^L ;  or  10  =  ^  ;  hence  W  =  320 Ibs. 
2 

7.  Application  of  the  pulley. — ~N"o  mechanical  advan- 
tage is  gained  by  the  use  of  the  fixed  pulley,  because 
the  weight  must  move  just  as  fast  as  the  power,  jet  it 


124 


NATURAL    PHILOSOPHY. 


is  of  great  value  in  the  arts,  for  changing  the  direction 
of  forces.  A  sailor  standing  upon  the  deck  of  his  ship 
may,  by  the  use  of  a  fixed  pulley,  hoist  the  sail  to  the 
top  of  the  loftiest  mast ;  or  when  heavy  bales  or  boxes 
are  to  be  lifted  to  the  upper  floors  of  warehouses,  a 
horse,  trotting  along  the  level  yard  or  street  (Fig.  55), 
will  lift  them  as  effectually  as  though  he  were  able  to 
climb  the  perpendicular  wall  with  the  same  rapidity. 

The  movable  pulleys  with  single  rope,  are  in  common 
use  for  moving   heavy  weights  through  considerable 
distances.     Merchandise  may  be  lifted  by  means  of 
Fig.  65.  them,  from  the  hold  of  a  ship 

to  the  wharf,  or  to  the  upper 
stories  of  store -houses  ;  or  by  a 
different  arrangement  of  the 
machine,  the  ship  itself  may 
be  drawn  from  the  water  for 
repairs.  In  practice,  the  fixed 
pulleys  of  a  system  are  placed 
side  by  side,  and  thus  form 
what  is  called  a  block:  the 
movable  pulleys,  likewise  side 
by  side,  form  another  block. 
By  this  means  the  system  is 
made  compact. 

In  all  pulleys  there  is  a  loss 
of  power,  due  to  the  friction 
of  the  pulleys  in  the  blocks,  to  the  weight  of  the 
lower  block,  and  to  the  stiffness  of  the  ropes  used ;  so 
that  the  weight,  actually  overcome  by  a  given  power,  is 
al\\  ays  less  than  the  laws  of  equilibrium  would  afford. 


(34.)  The  principle  of  momentum  applied  to  the  in- 
clined  plane  shows  : — 


NATURAL    PHILOSOPHY. 


V25 
r/tb 


1st. — That,  when  the  power  acts  parallel  to  the  If 
of  the  plane,  the  power  and  weight  will  be  in  r/ni 
librium  when  the  power  is  to  the  weight  as  the  \  /r/jht. 
of  the  plane  is  to  its  length; 

2d. — That,  if  the  power  acts  parallel  to  the  base  c  i  the 
plane,  the  power  and  weight  will  be  in  equilibrium 
when  the  power  is  to  the  weight  as  the  height  of  the 
plane  is  to  its  base. 

The  applications  of  this  machine  are  very  numerous. 

1.  The  inclined  plane. — Any  plane,  hard  surf*,;e, 
placed  in. an  oblique  position,  may  be  used  as  an  inclii  >nd 
plane.  In  Fig.  56,  A  B  represents  an  inclined  plan*. 

Fig.  66, 


The  distance  B  C,  is  the  height  of  the  plane,  and  A  0  13 
its  base.  The  weight  W,  may  be  urged  up  the  plane 
by  a  force  acting  parallel  to  A  B,  or  parallel  to  A  C,  or 
at  any  angle  to  these.  We  are  to  notice  the  first  two 
cases  only. 

2.  If  the  power  acts  parallel  to  the  length  of  the 
plane. — In  the  figure  the  power  P,  by  means  of  a  rope 
going  over  the  fixed  pulley  D,  at  the  top  of  the  plane, 
acts  upon  the  weight  W,  in  a  direction  (W  D)  parallel 
to  the  length  A  B,  of  the  plane. 

Now,  a  force  which  will  urge  the  weight  from  A  to  B, 


126 


NATURAL    PHILOSOPHY. 


is  lifting  it  only  through  the  vertical  height,  C  B.  But 
while  the  weight  goes  from  A  to  B,  the  rope  passing 
over  the  pulley,  will  let  the  power  down  a  distance 
equal  to  A  B,  in  the  same  time.  The  velocity  of  the 
weight  may,  therefore,  be  represented  by  the  line  C  B, 
and  the  velocity  of  the  power  by  the  line  A  B.  The 
momentum  of  the  power  is,  therefore,  P  x  A  B ;  that 
of  the  weight,  "W  x  C  B.  When  these  momenta  are 
equal,  the  two  forces  will  be  able  to  balance  each  other. 
Thus:— 

P  x  A  B  =  W  x  C  B ;  or 

P  :  W  : :  C  B  :  A  B. 

This  proportion  teaches  us  that,  when  in  equilibrium,  the 
power  is  to  the  weight  as  the  height  of  the  plane  is  to  its 
length. 

Fig.  5T. 


If,  for  example,  the  height  C  B,  is  4  feet,  and  the 
length  of  the  plane  A  B,  is  16  feet,  a  power  of  1  Ib.  will 
balance  a  weight  of  4  Ibs.  For — 

lib.  :  4 Ibs.  ::  4ft.  :  16ft. 


NATURAL    PHILOSOPHY. 

3.  If  the  power  acts  parallel  to  the  ~base  of  the  plane. 
— Let  A  B,  Fig.  57,  represent  a  plane  whose  height  ia 
C  B,  and  whose  base  is  A  C.     The  power  acts  upon  the 
weight  bj  means  of  a  cord  passing  over  the  pulley  at  C, 
in  a  direction  parallel  to  A  C.     To  move  the  weight 
from  A  to  B,  will  be  lifting  it  only  through  the  verti- 
cal height,  C  B.     If  the  pulley  C,  could  be  raised  while 
the  weight  goes  up,  so  as  to  keep  the  cord  parallel  to 
A  C,  then  the  cord,  passing  over  the  pulley,  will  let  the 
power  down  a  distance  equal  to  A  C.     The  line  C  B, 
represents  the  velocity  of  the  weight,  and  A  C  the  ve- 
locity of  the  power.     The  momentum  of  the  power  ia 
therefore  P  x  A  C,  and  that  of  the  weight,  W  x  C  B. 
If  now,  these  momenta  are  equal,  the  power  and  weight 
will  just  balance  each  other.     Hence — 

P  x  A  C  =  W  x  BC;or 
P  :  W  : :  B  C  :  A  C. 

From  thiw  proportion  we  learn  that,  when  the  power 
acts  parallel  to  the  base  of  the  plane,  the  power  and 
weight  will  ~be  in  equilibrium  when  the  power  is  to  the 
weight  ax  the  height  of  the  plane  is  to  its  lose. 

Thus,  if  the  height  of  the  plane  is  2  ft.  and  the  base 
is  10  fb.,  a  power  of  1  Ib.  will  balance  a  weight  of  5  Ibs. 
For  lib.  :  5 Ibs.  ::  2ft.  :  10ft. 

4.  Application  of  the  inclined  plane. — This  machine 
is  used  to  lift  heavy  weights  through  short  distances. 
Many  familiar  examples  might  be  named.     If  a  barrel 
of  merchandise  is  to  be  placed  upon  a  wagon,  it  is  often 
rolled  up  on  a  plank,  one  end  of  which  rests  upon  the 
ground,  tho  other  upon  the  wagon.     A  hogshead  which 
a  dozen  men  could  not  lift,  may  thus  be  loaded  by  the 
strength  of  one  or  two. 

Our  common  stairs  are,  in  principle,  inclined  planes, 


128  NATURAL    PHILOSOPHY. 

the  arrangement  of  steps  only  giving  a  firm  footing.  If 
the  distance  between  the  floors  be  f  the  length  of  the 
stairs,  then,  besides  the  <  rdinary  effort  of  walking,  the 
person  must  continually,  while  going  up,  labor  to  lift  £ 
of  the  weight  of  his  body. 

(35.)  The  wedge,  in  its  most  common  form,  is  made 
up  of  two  inclined  planes  joined  together  at  their  bas^s. 
The  sharper  the  wedge,  the  greater  the  resistance  which 
may  be  overcome  by  it. 

1.  The  Wedge. — This  instrument  is  shown  in  use  by 
Fig.  58.  A  B  is  called  the  back  of  the  wedge :  A  c 
and  B  <?,  are  its  sides,  and  c  is  its  edge. 
It  is  generally  used  in  cleaving  timber,  and 
sometimes  for  raising  heavy  weights  through 
very  short  distances.  For  these  purposes  its 
edge  is  put  into  a  crevice  made  for  it,  and 
it  is  then  driven  by  blows  with  a  sledge. 

Since  we  can  not  calculate  the  force  of  a 
blow,  no  attempt  will  be  here  made  to  es- 
tablish any  law  of  equilibrium. 

(36.)  The  principle  of  momentum  applied  to  the 
screw,  shows  that : — 

The  power  and  weight  will  be  in  equilibrium,  when 
the  power  is  to  the  weight,  as  the  distance  between  two 
contiguous  threads  is  to  the  circumference  of  the  circle 
in  which  the  power  moves. 

The  screw  is  used  extensively  to  produce  great  press- 
ure :  it  is  often  used  to  measure  delicate  distances. 

1.  The  screw.— The  screw  consists  of  a  cylinder  of 
wood  or  metal,  with  a  spiral  groove  winding  around 
its  circumference  This  grooved  cylinder  (C,  Fig.  59) 


NATURAL    PHILOSOPHY 


129 


passes  through  a  block  N  G,  on  the  inside  surface  of 
which  is  a  spiral  groove,  into  which  the  raised  parts 
of  the  cylinder  exactly  fit.  The  block  is  usually 
called  the  nut.  The  raised  parts  between  the  grooves 
of  the  cylinder  are  called  the  threads. 

Suppose  the  nut  to  be  stationary,  then,  if  the  screw 
is  turned  by  a  power  acting  upon  the  lever  at  B, 
it  must  advance  downward  at  every  revolution,  and 
the  pressure  of  the  advancing  screw  will  be  exerted 
upon  any  object  placed  Fig.  59. 

under   the   press-board,  "inir    1 

E  F,  against  which  the 
end  of  the  screw  presses. 

2.  Application  of  the 
principle  of  momen- 
tum.— By  one  turn  of 
the  screw,  it  will  ad- 
vance downward  a  dis- 
tance just  equal  to  the 
distance  between  two 
contiguous  threads.  The 
press-board  E  F,  which 
may  be  regarded  as 
the  weight,  will  be 
moved  along  through  Q 
a  distance  equal  to  a  J,  by  every  turn.  The  power 
acting  at  B  will,  in  the  same  time,  move  through  the 
circumference  of  the  circle  whose  radius  is  B  C.  These 
distances,  through  which  the  power  and  weight  pass  in 
the  same  time,  may  represent  their  velocities.  Hence 
the  momentum  of  the  power  will  be  P  x  Circumference 
of  the  circle  whose  radius  is  B  C,  and  that  of  the  weight 
will  be  W  x  a  b.  If  these  momenta  are  equal,  the  two 

6* 


130  NATURAL    PHILOSOPHY. 

forces,  when  at  rest,  will  be  in  equilibrium.     Hence: — 
P  x  Circ.  BC  =  Wxa&;or 
P  :  W  ::  al  :  Circ.  B  C. 

This  proportion  teaches  that  the  power  and  weight 
will  be  in  equilibrium  when  the  power  is  to  the  weight, 
as  the  distance  between  two  contiguous  threads  is  to  the 
circumference  of  the  circle  in  which  the  power  moves. 

Thus,  if  the  distance  between  the  threads  is  -J  in.,  and 
the  circumference,  traveled  by  the  power,  is  5ft.,  or  60  in., 
what  weight  on  the  nut,  would  1  Ib.  power  at  B  balance  ? 
1  Ib.  :  W  : :  J  in.  :  60  in.  W  =  120  Ibs. 

3.  Application  of  the  screw.  —  The  screw  is  used 
when  great  weights  are  to  be  lifted  short  distances, 
or  when  heavy  pressure  is  to  be  exerted.  By  its  use, 
cotton  is  pressed  into  bales,  the  juices  of  fruits  extracted, 
and  oils  pressed  from  vegetable  bodies,  such  as  linseed 
and  the  almond. 

In  contrast  with  these  uses  of  the  screw,  depending  on 
the  immense  pressure  it  can  exert,  is  another,  remarkable 
for  its  delicacy.  It  is  used  to  measure  very  small  dis- 
tances when  accuracy  is  required.  Screws  with  threads 
of  exceeding  fineness  are  used  for  this  purpose.  Sup- 
pose a  screw  with  100  threads  in  one  inch  of  its  length ; 
then,  at  every  turn  its  end  would  advance  just  -^  of  an 
inch,  and  if  it  carry  a  steel  marker,  spaces  of  that  length 
may  be  marked  off  on  any  body  along  side  of  which  it 
moves.  Now  let  the  power  move  in  a  circle  10  in.  in 
circumference,  and  let  this  circle  be  graduated  to  inches, 
tenths,  and  hundredths.  If  the  power  move  one  inch 
on  this  scale,  the  marker  on  the  end  of  the  screw  will 
go  forward  only  TTnnj  of  an  inch.  If  the  power  goes 
YJJ-  inch,  then  the  marker  will  advance  only  10000  of  an 
inch,  a  distance  quite  too  small  to  be  seen  except  by 


NATURAL    PHILOSOPHY. 

the  aid  of  a  good  microscope.  Astronomers  use  the 
micrometer  screw  to  measure  the  apparent  sizes  of  the 
heavenly  bodies. 

PROBLEMS   ILLUSTRATING    THE   THEORY   OF   MACHINERY. 

Vl.  Suppose  a  body  weighing  5  Ibs.  moves  without 
resistance,  with  a  velocity  of  20  ft.  a  second :  what  mo- 
mentum would  it  have  ?  Ans.  100. 
^  2.  Suppose  the  body  weighing  5  Ibs.  moves  against 
resistance,  with  a  velocity  of  20  ft.  a  second,  kept 
uniform  by  a  constant  force :  what  would  be  its  living 
force  ?  Ans.  2,000. 

*'  3.  Suppose  two  bodies,  one  of  5  Ibs.,  the  other  of 
Y  Ibs.  move,  with  equal  velocities,  100  ft.  a  second,  but 
in  opposite  directions,  without  resistance.  Let  them  at 
the  same  instant  strike  a  third  body :  in  which  direc- 
tion would  the  body  be  moved,  and  with  what  force  ? 

Ans.  to  %d  question,  200  Ibs. 

^  4.  Two  trains  of  cars,  each  moving  at  the  rate  of  30 
miles  an  hour,  or  4A  ft.  a  second,  one  weighing  10  tons, 
the  other  20  tons,  come  in  collision  from  opposite  di- 
rections :  what  force  would  be  exerted  to  dash  them  to 
pieces?  Ans.  58,080  tons  a  second. 

5.  If  a  power  of  10  Ibs.  act  upon  the  long  arm  of  a  le- 
ver, a  distance  from  the  fulcrum  of  6  ft. :  what  weight 
would  it  balance  at  a  distance  of  2  ft.  on  the  other  side 
of  the  fulcrum  ?  Ans.  30  Ibs. 

6.  In  a  lever  of  the  second  class,  the  power,  3  Ibs.,  is 
at  a  distance  of  1  ft.  from  the  fulcrum :  what  weight 
will  it  balance  at  a  distance  of  1  in.  from  the  fulcrum  ? 

Ans.  36  Ibs. 
Y.  In  a  compound  lever,  the  long  arms  are  4  ft,  5  ft., 


132 


NATURAL    PHILOSOPHY. 


and  6  ft.  in  length;  the  short  arms  are  l'ft.,  2  ft.,  and 
3  ft.  long  :  a  weight  of  2,000  Ibs.  is  to  be  balanced  :  how 
much  power  must  act  upon  the  first  long  ara  ? 

Ans.  100  Ibs. 

8.  A  power  of  10  Ibs.  lifts  a  weight  of  500  Ibs.  by 
means  of  a  lever  whose  short  arm  is  1  ft.  long :    how 
long  is  the  long  arm  of  the  lever?  Ans.  50  ft. 

9.  If  the  500  Ibs.  in  the  last  example  is  to  be  lifted 
2ft.,  how  far  must  the  power  move  to  do  it? 

Ans.  100  ft. 

10.  The  radius  of  a  wheel  is  30  inches ;  of  its  axle, 
5  inches  :    a  power  of  100  ounces  is  exerted  upon  the 
wheel :  how  much  weight  will  it  balance  at  the  axle  ? 

Ans.  600  oz. 

11.  Three  wheels  and  axles  are  combined,  as  shown 
in  Fig.  50 ;  the  radius  of  each  wheel  is  20  inches ;  of  each 
axle,  is  4  inches  ;  a  power  of  2  pounds  acts  on  the  first 
wheel :  what  weight  will  it  balance  on  the  last  axle  ? 

Ans.  250  Ibs. 

*-12.  A  force  of  16  Ibs.  is  applied  to 
the  last  axle  (Fig.  50),  and  moves  at 
the  rate  of  10  inches  a  second:  how 
much  weight  at  the  first  wheel  would 
balance  it  at  rest?  and  how  much 
slower  will  it  go  when  in  motion  ? 

Ans.  .128  Ib. ;  T£  ras  fast. 
13.  With  a  single  movable  pulley  a 
stone  weighing  350  Ibs.  is  to  be  lifted : 
what  power  must  be  exerted  ? 

Ans.  175 -Fibs. 

u!4.  With  the  single  movable  pulley, 
shown  in  Fig.  60,  what  power  at  P  would  balance  a 
weight  of  250  Ibs.  at  W  ?  Ans.  83J  Ibs. 


Fig.  60. 


NATURAL    PHILOSOPHY.  133 

V  15.  If  the  weight  W,  is  lifted  by  the  power,  how 
far  would  the  power  move  to  lift  the  weight  1  ft.  ? 

Ans.  3  ft. 

16.  In  a  system  of  4  movable  pulleys,  with  a  single 
rope,  what  power  would  be  needed  to  balance  a  weight 
of  500 Ibs?  Ans.  62 Jibs. 

17.  Suppose  each  of  the  4  pulleys  has  a  separate  rope, 
what  power  would  then  be  needed?       Ans.  31 J  Ibs. 

18.  An  inclined  plane,  6  ft.  in  length  and  2  ft.  high, 
is  used  to  put  a  barrel  of  flour  upon  a  cart.     The  bar- 
rel weighs  196  Ibs. :  how  much  force  must  a  man  exert, 
pushing  parallel  to  the  length  of  the  plane  ? 

Ans.  65^+lbs. 

19.  If  the  base  of  the  plane  were  5ft.,  its  height 
2ft.,  and  the  man   pushes  parallel  to  the  base,  how 
much  force  must  he  exert  to  lift  the  barrel  of  flour  ? 

Ans.  78f  +  lbs. 

20.  The  distance  between  the  threads  of  a  screw  is 
1  in.,  and  the  power  of  25  Ibs.  moves  in  a  circle  of  3  ft. 
in  circumference :   how  much  weight  will  it  balance  ? 

Ans.  900  Ibs. 

21.  A  power  of  20  Ibs.,  0y  means  of  a  screw,  exerts  a 
pressure  of  800  Ibs.     The  threads  are  £  in.  apart :  what 
is  the  circumference  of  the  circle  in  which  the  power 
moves?  Ans.  20  inches. 

§   5.    OF  THE   MOTION   OF   LIQUIDS. 

(37.)  Water  will  issue  from  an  opening  in  the  side 
of  a  vessel  with  the  same  velocity  which  a  body  would 
gain  by  falling  from  the  surface  of  the  water  to  the 
center  of  the  opening. 

Hence  the  velocity  of  the  jet  of  water,  will  depend 
only  on  the  distance  of  the  orifice  below  the  surface  of 


134-  NATURAL    PHILOSOPHY. 

the  water  in  the  vessel,  and  may  be  calculated  by  the 
formula,  Y  =  2  V!Sg. 

1.  The  velocity  of  a  jet  of  water  the  same  as  that  of 
a  falling   "body. — To   prove    this   principle,  we  must 
remember :    first,  that  water,  confined  in  pipes,  will 
rise  as  high  as  the  source  from  which  it  comes    [see 
(11.)   1]  ;   second,  that  a  body  thrown  upward,  starts 
with  the  same  velocity  that  it  has  when  it  gets  back. 
(See  p.  94.) 

In  Fig.  61,  a  bent  tube  (A)  extends  from  near  the 

Fl'g- 61-  bottom  of  a  vessel  of  water. ' 

The  water  rises  as  high  in 
the  tube  as  in  the  vessel  ;  it 
is  the  upward  pressure  of 
the  water  at  A  that  pushes 
up.  The  same  force 
would  be  exerted  on  the 
water  at  A,  if  the  tube 
were  cut  off  at  that  point, 
and  it  would,  it'  not  resisted,  throw  the  water  to 
the  same  height,  as  shown  on  the  other  side  of  the  fig- 
ure, at  B.  But  the  velocity  with  which  it  must  start 
from  B  to  reach  the  level  of  K,  is  the  same  it  would 
gain  by  falling  from  that  level  back  to  B.  If  the  tube 
were  cut  off  at  C,  the  water  would  issue  with  the  same 
force,  and,  therefore,  with  the  same  velocity.  Hence 
the  velocity  with  which  the  water  issws,  is  the  same  as 
that  of  a  ~body  falling  from  the  surface  of  the  water 
down  to  the  center  of  the  orifice. 

2.  The  velocity  of  the  jet  depends  on  the  distance 
of  the  orifice  lelow  the  level  of  the  water. — The  ve- 
locity of  a  falling  body  depends  only  on  the  height  from 
which  it  has  fallen.     All  bodies,  whatever  be  their  size 


NATURAL    PHILOSOPHY.  135 

oi  nature,  fall  with  equal  velocities.  In  the  same  man 
ner,  all  liquids,  however  different  in  nature,  will  issue 
with  equal  velocities,  if  the  openings  from  which  the^ 
are  thrown  are  at  the  same  distance  from  the  surface 
of  the  liquid  in  the  reservoir. 

3.  Velocity  calculated  ~by  the  formula ,  Y  —  2  VSg. — • 
Now,  the  velocity  of  a  falling  body  is  given  by  the  equa- 
tion Y  =  2  !/&?.  [see  (24,)  6],  and  it  is  clear  that  the 
velocity  of  a  jet  of  water  will  be  given  by  the  same  for- 
mula, if  S  represents  the  distance  of  the  orifice  below 
the  level  of  the  water  in  the  vessel. 

If,  for  example,  we  would  know  the  velocity  of  a  jet 
of  water  from  an  orifice  36  feet  below  the  surface  in 
a  reservoir,  we  put  36  for  S  in  the  formula.  It  then 
reads  Y  =  2  V3G  x!6.  The  value  of  Y  is,  then,  48  ; 
the  velocity  of  the  water  is  48  feet  a  second. 

(38.)  The  quantity  of  water  discharged  from  an  on 
fice,  depends  upon  its  velocity,  the  size  of  the  orifice, 
and  the  time  of  flow.  It  may  be  found  by  multiplying 
the  values  of  these  three  things  together. 

1.  To  calculate  the  quantity. — If  the  orifice  have  an 
area  of  1  sq.  ft.,  then  the  velocity  will  represent  the 
number  of  cubic  feet  discharged  in  one  second.  Multi- 
plying this  by  the  number  of  square  feet,  or  fraction  of 
a  square  foot  in  the  orifice,  must  show  the  number  of 
cubic  feet  flowing  from  the  orifice  in  one  second,  and 
this  multiplied  by  the  number  of  seconds,  will  tell  the 
number  of  cubic  feet  discharged.  For  example,  how 
much  water  will  flow  from  an  orifice  of  1|  sq.  ft.  area, 
at  a  depth  of  9  ft.  below  the  surface  of  the  water,  in  10 
seconds  1  At  a  depth  of  9  ft.  the  water  will  issue  with 


136  NATURAL    PHILOSOPHY. 

a  velocity,  Y  =  2  1/9^16  =  24  ft.  Now,  if  the  open 
ing  was  one  square  foot,  then  24  cubic  ft.  would  issue  in 
one  second,  and  24  x  1£  x  10  —  360  cubic  ft.  must  issue 
from  the  orifice  of  1^-  sq.  ft.  in  the  given  time,  10  seconds. 
The  rule  is  concisely  expressed  by  the  formula : — 

Q  =  YxAxT,  in  which 
Q  represents  the  quantity  of  water  discharged, 
Y          "          "    Velocity, 
A  "    Area  of  the  orifice, 

T         "          "    Time  of  flow. 

In  this  equation  there  are  four  things,  and  it  is  clear 
that,  any  three  of  them  being  given,  the  fourth,  which- 
ever it  may  be,  can  be  found.  A  single  illustration 
will  show  how  this  is  done. 

Suppose  10,000  cubic  ft.  of  water  must  be  discharged 
in  60  seconds,  from  an  orifice  so  far  below  the  surface 
of  the  water  that  the  velocity  of  the  jet  is  250  ft.  a 
second  :  how  large  must  the  orifice  be  made  ? 

In  this  problem,  the  value  of  Y  is  given,  250  ft. ;  the 
value  of  T  is  60  seconds ;  the  value  of  Q  is  10,000  cubic 
ft. ;  the  value  of  A  is  wanted.  By  putting  the  given 
values  into  the  equation  it  becomes  : — 

10,000  =  250  x  A  x  60  ;  hence, 
A  :=  f  sq.  ft.,  or  96  sq.  in. 

(39.)  The  velocity  of  a  jet  of  water  and  the  quantity 
discharged  are  found  in  practice  to  be  much  less  than 
the  foregoing  theory  would  give.  The  actual  amount 
may  be  increased  by  using  short  tubes  of  different 


1.  TJie  velocity  in  practice   less   than  in  theory. — • 
If  the  experiment  be  tried  with  a  vessel  of  water,  aa 


NATURAL    PHILOSOPHY'.  137 

shown  by  Fig.  61,  it  will  be  seen  that  the  jot  does  not 
rise  quite  as  high  as  the  level  of  the  water  in  the  vessel. 
It  does  not,  because  the  resistance  of  the  air  pi  events 
it.  From  any  orifice,  water  must  issue  against  the  re- 
sistance of  air,  and  its  motion  is  less  rapid  on  that 
account. 

2.  The  quantity  in  practice  less  than  in  theory. — 
If  we  examine  a  jet  of  water  flowing  from  an  orifice  in 
the  side  of  a  vessel,  we  will  see  that  it  grows  rapidly 
smaller,  so  that,  at  a  little  distance,  its  size  is  only  about 
f  as  great  as  at  the  orifice.     Beyond  this  point  the  con- 
traction of  the  jet  is  gradual.    The  rapid  contraction 
near  the  orifice  is  due  to  cross  currents,  caused  by  the 
water  flowing  toward  the  orifice  from  difl'erer',  direc- 
tions in  the  vessel ;  these  currents  may  be  seen  if  there 
be  any  solid  particles  floating  in  the  water.     If  the  jet 
were  the  size  of  the  orifice,  the  quantity  of  water  dis- 
charged would  be  what  the  theory  gives,  but  since  it  is 
only  about  two-thirds  as  large,  there  wil]  be  only  about 
two-thirds  as  much  water  discharged. 

3.  The  quantity  increased    ~by  usin$    tubes. — Short 
tubes  inserted  in  the  orifice  are  found  to  increase  the 
actual  flow.      T  lese  tubes   are  either  cylindrical  or 
conical. 

It  is  found  that  a  cylindrical  tube,  whose  length  is 
not  more  than  four  times  its  diameter,  if  placed  in  the 
orifice,  will  increase  the  amount  discharged  to  about 
.82  of  that  which  theory  gives.  In  this  case  the  water 
adheres  to  the  sides  of  the  tube,  so  that  the  contraction 
of  the  jet  is  prevented  ;  the  jet  is  the  size  of  the  orifice. 
By  the  use  of  conical  tubes  the  amount  discharged  may 
be  made  still  greater.  (See  Silliman's  Physics,  pp.  1 74. 
and  180). 


138 


NATURAL    PHILOSOPHY. 


(40.)  "Water-wheels  are  turned  by  the  power  of  mov 
ing  water.     There  are  several  kinds  :  First,  the  under- 
rig.  62.  shot     wheel ;     second, 

the  overshot  wheel; 
third,  the  breast 
wheel  ;  fourth,  the 
turbine  wheel. 

1.  The  undershot 
wheel. —  The  under- 
shot wheel  is  shown  in 
Fig.  62.  Its  circumfer- 
ence is  provided  with 
float  -  boards  a  ~b  c, 
against  which  the  run 
ning  water  acts.  Other  wheels  are  connected  with  the 
axle  of  this  one  by  cogs  and  bands.  This  form  of  wheel 
is  often  placed  in  a  horizontal  position,  and  water  from 

Fig.  63. 


tne  bottom  of  a  dam  guided  against  the  float-boards  of 
one  side. 
2    The  overshot  wheel. — The  overshot  wheel  (Fig.  63j 


NATURAL    PHILOSOPHY. 


139 


differs  from  the  undershot,  by  having  buckets  upon  it? 
circumference,  instead  of  float-boards.  The  water  en 
ters  the  buckets  at  the  top  of  the  wheel,  and,  filling 
those  on  one  side  of  it,  turns  the  wheel  by  its  weight. 
The  backets  all  open  in  the  same  direction,  so  that 
while  those  on  one  side  of  the  wheel  are  full,  those  on 
the  other  side  will  be  bottom  upward  and  empty. 

3.  The    Ireast    wheel— The  breast  wheel  (Fig.  64) 
differs  from  the  undershot   wheel   only  by  being  so 

Fig.  &4. 


placed  in  front  of  a  dam,  that  the  water  shall  fall  upon 
the  float-boards  of  its  circumference  on  a  level  with  its 
axis.  / 

4.  The  American  turbine. — The  construction  of  the 
turbine  is  more  complex  than  the  wheels  just  de- 
scribed. Its  action  may  be  understood  by  a  careful 
study  of  Fig.  65. 

This  figure  shows  a  section  of  the  interior  of  the 
wheel,  as  it  would  appear  to  one  who  looks  down 
upon  it  as  it  lies  in  its  horizontal  position.  In  the 
center  is  a  circular  disk  of  cast  iron,  A  B,  in  a  hori- 
zontal position.  •  On  the  upper  surface  of  this  disk 


NATURAL    PHILOSOPHY. 

«• 

are  fastened  the  curved  guides,  a  a  a.     This  disk  \* 
stationary.    The  wheel  proper,  C  D,  revolves  outside  of 
this  disk.     It  consists  of  two  cast-iron  plates,  one  above 
rig.  65.  the  other,  the  space  be 

tween  them  being  di- 
vided into  numerous 
channels  by  the  curved 
partitions,  c  c  c.  The 
partitions  in  the  wheel, 
and  the  guides  on  the 
disk,  are  curved  in  op- 
posite directions.  To 
the  under  plate  of  this 
wheel  is  fastened  a  cast 
iron  plate,  which  ex- 
tends under  the  cen- 
tral disk  A  B,  and  to  the  center  of  this  plate  is  at- 
tached a  vertical  shaft  which  comes  up  through  the 
disk  at  E. 

The  turbine,  except  the  upper  part  of  the  shaft,  is 
entirely  vnder  water.  The  weight  of  the  column  of 
water  above  the  disk  forces  the  water  with  great  power 
and  force  out  from  between  the  curved  guides  of  the 
disk,  into  the  curved  channels  of  the  wheel,  in  as 
many  different  streams  as  there  are  spaces  between  the 
guides.  The  force  of  these  streams,  striking  against 
the  partitions  of  the  wheel,  turns  the  wheel  in  the 
direction  indicated  by  the  arrow.  The  vertical  shaft 
turns  with  the  wheel,  and,  by  means  of  cogs,  gives 
motion  to  other  parts  of  the  machinery.  (See  Silli- 
man's  Physics,  p.  184.) 

Of  all  forms  of  water-wheel,  the  turbine  is  most  en- 
ergetic and  economical. 


NATURAL    PHILOSOPHY. 


§    6.    OF    THE    MOTION    OF    AIR. 

(41.)  Air  in  motion  is  called  wind.  Winds  are  pro- 
duced by  the  action  of  heat  and  the  attraction  of  gravi- 
tation upon  the  atmosphere  ;  and,  in  the  case  of  the 
trade  winds,  partly  by  the  rotation  of  the  earth  on  its 
axis. 

1.  Wind.  —  The  motion  of  air,  called  wind,  is  due  to 
a  difference  in  the  temperature  of  two  portions  of  the 
atmosphere.  Heat  expands  air.  One  hundred  cubic 
inches  of  hot  air  will  weigh  less  than  a  hundred  cubic 
inches  of  cold  air.  Now,  if  a  portion  of  hot  and  light 
air  is  surrounded  by  that  which  is  colder  and  heavier, 
it  will  rise,  for  the  same  reason  that  a  cork  rises  in 
water.  It  will  be  pushed  up  out  of  the  way  by  the 
heavier  air,  which  takes  its  place. 

Let  us  now  suppose  that,  in  some  particular  part  of 
the  country,  the  air  becomes  heated  more  than  in  sur- 
rounding portions.  This  heated  and  lighter  air  will  be 
pushed  up  by  air  moving  in  from  all  directions  to  take 
its  place.  This  moving  air  is  wind.  People  residing 
north  of  the  heated  place  will  observe  a  north  wind, 
and  those  south  of  it  a  south  wind. 

Now,  there  is  an  unequal  distribution  of  heat  over 
the  surface  of  the  earth.  It  is  caused  partly  by  the 
changes  of  the  seasons,  and  partly  by  various  local 
causes.  To  it  the  production  of  winds  is  due.  Their 
direction  will  be  modified  by  many  causes  :  the  form  of 
the  surface  over  which  they  pass  is  an  important  one. 
As  the  same  wind  often  blows  in  different  directions  on 
different  sides  of  a  house  ;  or,  as  blocks  of  buildings 
compel  the  wind  to  sweep  up  and  down  the  various 
streets  of  a  city,  so  the  hills  and  valleyp  of  a  country,  01 


14:2  NATURAL    PHILOSOPHY. 

the  presence  of  forests  or  plains,  will  modify  the  direc 
tion  of  the  winds  that  blow  over  them. 

2.  The  trade  winds. — The  trade  winds  require  par 
ticular  notice.     They  occur  in  the  equatorial  parts  of 
the  earth,  and  always  blow  in  the  same  directions.    Over 
a  surface  of  about  30°  of  latitude  on  the  north  side  of 
the  equator,  they  blow  from  the  northeast  toward  the 
southwest ;  while  south  of  the  equator,  over  about  the 
same  width  of  zone,  they  blow  from  the  southeast  to- 
ward the  northwest.     These  directions  are  maintained 
so  constantly,  that  mariners  count  upon  the  trade  winds 
with  almost  the  same  certainty  as  upon  the  rising  and 
setting  of  the  sun. 

3.  Due  to  heat  and  the  rotation  of  the  earth. — To 
explain  this   phenomenon  we  must  remember:  first, 
that  the  equatorial  region  is  constantly  heated  by  the 
sun  more  than  parts  of  the  earth  either  north  or  south ; 
and  second,  that  the  earth  revolves  from  west  to  east, 
the  equatorial  parts  moving  most  swiftly. 

The  heated  air  at  the  equator,  lighter  than  the  air 
either  north  or  south  of  it,  will  be  pushed  up,  while 
currents  of  colder  air  from  the  north  and  from  the 
south,  will  move  toward  the  equator.  But  the  equa- 
torial parts  of  the  earth  move  toward  the  east  more 
swiftly  than  other  parts ;  the  air  from  the  north  must, 
therefore,  pass  ovei  portions  of  the  earth  which  move 
eastward  faster  than  itself,  and  it  will  be  left  behind. 
We  find,  then,  that  there  is  a  real  motion  from  the 
north,  and  at  the  same  time  an  apparent  motion  from 
the  east ;  these  two  motions  combined  make  the  direc- 
tion of  the  wind  to  be  from  the  northeast.  A  similar 
explanation  will  show  why  the  southern  trade  wind 
blows  from  the  southeast  toward  the  northwest.  (See 
Silliman's  Physics,  p.  643.) 


NATURAL    PHILOSOPHY. 


CHAPTER     IV. 


OF  MOTION— (CONTINUED). 

IHTBODUCTION. APPLICATION   OF   THE   FUNDAMENTAL 

IDEAS. 

(42.)  Read  (4),  (7),  and  (20).— Attraction,  repulsion, 
and  inertia,  acting  upon  masses,  or  molecules,  produce 
vibrations. 

1.  Attraction,  repulsion,    and    inertia. — We    have 
seen  that  the  forces  of  nature  are  only  different  mani- 
festations of  attraction  and  repulsion.     [See  (20.)  1.] 
We  have  also  seen  that  a  body  in  motion  can  not  stop 
itself.     [See  (4.)  2.]    When,  therefore,  a  body  has  been 
put  in  motion,  by  any  force,  it  will  move  in  that  direc- 
tion, on  account  of  its  inertia,  until  stopped  by  an  oppo- 
site force.     Suppose  the  force  which  stops  it  continues 
its  action  afterward,  it  will  move  the  body  back  to  ward  its 
first  position,  and  then  if  the  force  cease,  the  inertia  will 
move  it  onward  until  again  stopped  by  an  opposite  force. 

2.  Vibrations. — The  body,   thus   acted   upon,   will 
swing  alternately  back  and  forth  over  the  same  path. 
Such  a  motion  is  called  vibration. 

If,  with  the  finger,  we  sink  one  scale-pan  of  a  balance, 


NATURAL    PHILOSOPHT. 

it  will  continue  to  pass  alternately  up  and  down  ovei 
the  same  path  for  a  long  time  after  the  finger  is  re- 
moved :  it  vibrates.  Or  if,  instead  of  pushing  it  down 
we  pull  the  scale-pan  to  one  side  and  then  let  go  of  it, 
it  will  swing  back  and  forth  for  a  long  time  ;  this  alter- 
nate motion,  to  and  fro,  is  vibration.  Suppose  a  ball, 
hung  by  a  fine  wire,  be  twirled  by  the  fingers  so  as  to 
twist  the  wire ;  let  go  of  it,  and,  speedily  untwisting 
the  wire,  it  will  go  on  for  a  time  twisting  it  up  the 
other  way.  The  ball  rotates,  first  in  one  direction  and 
then  in  the  other,  and  this  alternate  motion  is  vibration. 

Or  take  a  bent  glass  tube ;  pour  water  into  it  until 
the  arms  are  two-thirds  full ;  tip  it  to  one  side  and  then 
suddenly  bring  it  back  to  a  vertical  position.  The 
water  will  rise  and  fall  in  the  arms  of  the  tube,  and 
will  continue  this  alternate  motion  up  and  down  for 
some  time.  In  this  case  a  liquid  vibrates. 

Gases  may  be  made  to  vibrate  in  the  same  way. 

§  1.    OF   THE    VIBRATIONS    OF   THE    PENDULUM. 

(43.)  The  pendulum  vibrates  under  the  influence  ot 
gravitation  and  inertia.  Its  vibration  is  governed  by 
three  laws : — 

1st.  The  time  of  one  vibration  varies  as  the  square 
root  of  the  length  of  the  pendulum. 

2d.  The  time  of  one  vibration  varies  inversely  as  the 
square  root  of  the  force  of  gravity. 

3d.  The  time  of  one  vibration  is  independent  of  the 
length  of  the  arc  through  which  the  pendulum  vibrates. 

1.  Tke  pendulum.— A.  body  hanging  from  a  fixed 
point  by  a  flexible  cord  or  wire,  is  called  a  pendulum 


NATURAL    PHILOSOPHY. 


In  Fig.  66,  the  pendulum  is  represented  as  a  ball  B, 
hung  from  a  point  A. 

If  this  ball  be  lifted  from  the 
point  B  to  C,  and  then  loosed 
from  the  hand,  it  will  swing 
back  and  forth  through  the 
arc  D  C,  going  a  less  and  less 
distance,  until  finally  it  will 
Btop  at  B.  Its  motion,  from 
one  end  of  its  arc  D,  to  the 
other  C,  is  a  single  vibration, 
and  the  distance  D  C,  through 
which  it  vibrates  is  called  the 
amplitude  of  vibration. 

2.  It  vibrates  under  the  influence  of  gravitation  and 
inertia. — Suppose  a  ball  at  M  (Fig.  67),  to  represent  a 
pendulum  hung  from  the  fixed  point  Fig- 6T- 

C,  by  a  cord  M  C.  Now,  if  this  ball  be 
lifted  to  the  point  m,  and,  for  a  mo- 
ment, held  there,  the  force  of  gravity 
will  act  upon  it  in  a  vertical  direc- 
tion. We  will  represent  this  force 
by  the  line  m  A,  and  resolve  it  into 
two  components  [see  (26.)  1],  shown 
by  the  lines  m  I)  and  m  B.  The 
force,  m  B,  acts  lengthwise  of  the 
string  without  effect  to  move  the  ball : 
the  other  force,  raD,  at  right  angles  to  the  first,  will 
pull  the  ball  toward  the  point  M.  If  the  ball  is  allowed 
to  fall  to  M,  its  inertia  will  carry  it  beyond  that  point ; 
but  gravitation  will  then  be  pulling  it  back  with  just 
the  same  power  that  it  exerted  to  pull  the  ball  from  m 
to  M.  It  will  rise  from  M  to  n,  a  distance  just  as  far 
t 


146 


VATURAL  PHILOSOPHY. 


from  M,  as  it  lias  fallen  from  m.  It  will  there  st<rp , 
and  gravitation  will  bring  it  back  to  M,  while  its  iner- 
tia will  carry  it  up  to  m,  and  if  there  were  no  resistance 
to  its  motion  it  would  vibrate  forever  through  the  arc 
n  m.  The  resistance  of  the  air  and  the  friction  of  the 
cord  on  the  hook  will  finally  make  it  stop  at  M. 

3.  The  first  law. — If  two   pendulums   of  different 
lengths  (P  and  P1,  Fig.   68),  be  made  to  vibrate  to- 

gether,  the  short  one  will  be  seen  to 
vibrate  much  faster  than  the  other. 
We  learn  from  this  that  the  time  of 
vibration  depends  on  the  length  of  the 
pendulum. 

Now,  let  us  make  the  pendulum  P 
just  four  times  as  long  as  the  other. 
With  a  watch  in  the  hand,  we  can 
easily  count  the  number  of  vibrations 
it  makes  in  one  minute,  and  60  divi- 
ded by  this  number,  shows  how  long 
it  takes  to  make  one  vibration.  In  the 
same  way  we  can  find  the  time  it  takes 
the  shorter  pendulum  to  make  one  vi- 
bration. Doing  this,  we  find  that  the 
pendulum  P,  takes  twice  as  long  as 

the  other  to  vibrate  once.    Being  four  times  as  long  as 

the  other,  the  time  of  vibration  is  two  times  as  great. 

Hence,  the  time  of  one  vibration  varies  as  the  square 

root  of  the  length  of  the  pendulum. 

The  length  of  a  pendulum  to  vibrate  in  one  second 

is  about  39.1  inches;  to  vibrate  in  two  seconds,  it  must 

be  four  times  as  long ;  to  vibrate  in  one-half  a  second 

it  must  be  one-fourth  as  long. 

4.  The  second  law. — By   calculating  the   force   of 


NATURAL    PHILOSOPHY.  147 

gravity  (see  prob.  21,  p.  94),  at  different  distance? 
aboT  e  the  level  of  the  sea,  and  then,  by  experiment, 
finding  the  time  of  one  vibration  made  by  the  same 
pendulum  at  those  places,  it  will  be  found  that  the  time 
of  one  vibration  varies  inversely  as  the  square  root  of 
the  force  of  gravity. 

5.  The  third  law. — Finally,  if  we  make  the  pendu- 
lum P,  vibrate  in  a  large  arc,  and  find  the  time  of  one 
vibration,  and  then  make  it  vibrate  in  a  small  arc,  we 
shall  find  the  time  of  one  vibration  to  be  the  same. 
The  pendulum  must  vibrate  in  equal  times,  no  matter 
whether  its  arc  be  large  or  small.  In  other  words,  the 
time  of  one  vibration  is  independent  of  the  arc  through 
which  the  pendulum  vibrates. 

This  third  law  is  absolutely  true  only  when  the  arcs 
compared  are  very  small.  Yet,  in  the  latitude  of  Paris, 
it  is  found  that  for  a  pendulum  whose  length  is  one 
meter,  or  39.37  in.,  the  time  of  one  vibration,  through 
an  arc  of  8°,  is  only  .000076  of  a  second  longer  than  if 
its  arc  were  infinitely  small.  (See  Cooke's  Chem.  Phys. 
p.  69.) 

(44.)  These  laws  apply  to  a  single  point  in  a  pendu- 
lum, called  the  center  of  oscillation. 

1.  The  center  of  oscillation. — The  different  mole- 
cules of  a  pendulum  are  at  different  distances  from  the 
point  of  suspension,  and  hence  would  vibrate  in  differ- 
ent times  if  they  were  not  held  together  by  cohesion. 
Although  they  are  held  together,  and  must  all  move  at 
once,  yet  the  forces  that  would  make  them  vibrate  dif- 
ferently are  acting  just  the  same  as  if  they  were  not.. 
The  upper  parts  of  the  pendulum  are  trying  to  vibrate 
faster,  and  must  be  pulling  the  lower  parts  along ;  while 


148  NATURAL    PHILOSOPHY. 

the  lower  parts  are  trying  to  vibrate  slower,  and  must 
be  pulling  tlie  upper  parts  back.  There  must  be  some 
poiiit  in  the  pendulum,  at  which  these  two  struggles 
just  balance  each  other.  This  point  will  vibrate  just 
as  fast  as  if  it  were  influenced  by  no  other  molecules 
whatever.  A  point  in  the  pendulum  which  vibrates  as 
if  only  under  the  influence  of  its  own  gravitation  and 
inertia  is  called  the  center  of  oscillation.  The  center  of 
oscillation  is  generally  a  little  below  the  center  of  grav 
itj  of  the  pendulum  ball. 

2.  The  laws  apply  to  this  point. — The  three  laws, 
obtained  in  the  foregoing  paragraph,  apply  to  only  this 
point,  the  center  of  oscillation.  Indeed,  whenever  we 
speak  of  the  pendulum  we  refer  to  this  point.  By  the 
length  of  a  pendulum  we  mean  the  distance  from  the 
point  of  support  to  the  center  of  oscillation,  and  when 
we  use  the  term  vibration,  we  refer  to  the  motion  of 
this  one  point  of  the  pendulum. 

(45.)  There  are  several  uses  of  the  pendulum ;  we 
notice  only  two  : — 

1st.  It  is  used  to  measure  time. 

2d.  It  is  used  to  determine  the  form  of  the  earth. 

1.  Used  to  measure  time. — The  vibrations  of  a  pend- 
ulum are  made  in  equal  times.  If  then  we  know  the 
time  of  one  vibration,  and  can  count  the  number  made, 
we  know  the  time  during  which  the  pendulum  vibrates. 

Kow,  the  common  clock  is  an  instrument  in  which, 
by  weights,  friction  arid  the  resistance  of  air  are  over- 
come, so  that  the  pendulum  shall  continue  its  motion, 
and  by  which,  the  number  of  vibrations  are  at  the  same 
time  recorded  by  the  hands  moving  over  a  graduated 
dial. 


NATURAL    PHILOSOPHY.  149 

2.  Used  to  determine  the  form  of  the  earth. — The 
pendulum  has  been  used  to  determine  the  shape  of  the 
earth.  For  this  purpose,  pendulums  of  the  same  length 
have  been  made  to  vibrate  in  different  latitudes.  It 
has  been  found  that  the  time  of  one  vibration  is  lesa 
and  less  as  the  pendulum  approaches  the  poles  of  the 
earth.  Now,  to  make  the  vibrations  more  rapid,  the 
force  of  gravity  must  increase,  and  if  this  force  is 
stronger  toward  the  poles,  the  surface  of  the  earth 
must  be  nearer  the  center  of  the  earth  there  than  at 
the  equator.  The  polar  diameter  must,  therefore,  be 
shorter  than  the  equatorial  diameter,  and  the  shape  oi 
the  earth  must  be  that  of  an  oblate  spheroid. 

§  2.     OF    THE    VIBRATIONS    OF    COKDS. 

(46.)  The  vibrations  of  cords  are  due  to  the  action  of 
elasticity  and  inertia.  They  are  governed  by  three 
la  ws : — 

1st.  The  number  of  vibrations  in  a  second  varies  in- 
versely as  the  length  of  the  cord. 

2d.  The  number  of  vibrations  in  a  second  varies  di- 
rectly as  the  square  root  of  the  weight  by  which  the 
cord  is  stretched,  or  its  tension. 

3d.  The  number  of  vibrations  in  a  second  varies  in- 
versely as  the  square  root  of  the  weight  of  a  given 
length  of  the  cord. 

1.  The  vibration  of  cords. — Let  a  cord  or  string  be 
stretched  between  two  fixed  points  (a  and  #,  Fig.  69). 

Fig.  69. 


By  taking  hold  of  its  middle  point,  the  cord  may  be 


150  NATURAL    PHILOSOPHY. 

drawn  to  one  side,  a  c  b.  Then  loose  it,  and  it  will  spring 
back  and  go  an  equal  distance  on  the  other  side  a  d  b  ; 
then  return,  and  so  continue  to  swing  rapidly  back  and 
forth  until  it  finally  stops  in  its  first  position,  a  c  b. 

The  motion  of  the  cord  from  e  to  d  and  back  again, 
is  a  complete  vibration.  Its  motion  from  e  to  d,  is  a 
half  vibration,  or,  as  generally  called,  a  single  vibration. 
The  distance  from  e  to  d,  is  the  amplitude  of  vibration. 

2.  Due  to  elasticity  and  inertia. — When  the  force 
which  stretches  the  string  into  the  position  a  e  b,  is 
withdrawn,  elasticity  moves  it  back  to  its  first  position, 
a  G  b,  and  the  inertia  gained  by  this  motion,  throws  it 
forward  an  equal  distance,  to  a  d  b.     The  elasticity  of 
the  string  again  pulls  it  back  to  the  position,  a  c  b,  and 
its  inertia  carries  it  beyond,  and  thus,  under  the  joint 
influence  of  elasticity  and  inertia,  the  string  will  swiftly 
vibrate,  its  amplitude  growing  less  and  less,  on  account 
of  resistance,  until  at  last  it  stops  in  its  first  position. 

3.  The  laws  of  vibration. — The  vibrations  of  cords 
are,  in  all  cases,  quite  too  rapid  to  be  counted,  and 
yet  it  will  be  impossible  to  establish  any  laws  of  vibra- 
tion, unless  we  can  find  the  number  of  vibrations  made 
in  a  given  time.     How  can  this  be  done  ?  * 

However  rapid  the  motion  of  the  cord  may  be,  the 
lightning  swiftness  of  electricity  is  yet  greater  ;  so  the 
cord,  by  using  electricity,  may  register  the  vibrations 
which  it  makes. 

The  apparatus  used  for  this  purpose  by  the  author,  is 
shown  in  Fig.  70,  as  far  as  necessary  to  illustrate  the 
principle  of  the  process. 

*  The  syren  will  be  described  in  the  chapter  on  sound:  it  seems  de« 
sirable  here  to  make  the  cord  directly  register  its  own  vibrations,  so  that 
the  laws  of  vibration  shall  stand  independent  of  sound. 


NATURAL    PHILOSOPHY. 

A  <,  /id,  A  B,  rests  upon  the  two  bridges,  C  and  D 
Bud  pa  <?ikg  over  a  pulley,  B,  is  stretched  by  a  weight^ 
W.  Through  its  middle  point  is  a  fine  cambric  needle 
n,  just  \mder  the  point  of  which  stands  a  vessel  of  mer- 

Fig.  70. 


W 

cury,  M.  From  an  electrical  battery,  G,  one  wire  goes 
to  the  mercury,  and  another,  after  passing  around  an 
electro-magnet;  E,  is  threaded  into  the  eye  of  the  needle. 
At  P,  is  a  sharp  and  soft  pencil-point,  and  in  front  of  it 
is  a  roller  O,  over  which  passes  a  strip  of  paper. 

If  now,  the  string  vibrates  np  and  down,  the  point  of 
the  needle  will  come  in  contact  with  the  mercury  below 
it  at  the  end  of  every  vibration.  When  the  needle 
touches  the  mercury  the  electricity  darts  through  the 
wires,  and  the  magnet  E,  instantly  pulls  the  pencil-point 
against  the  paper,  and  a  dot  is  thereby  made.  • 

If  the  paper  le  drawn  along  in  front  of  the  pencil- 
point  while  the  string  is  vibrating,  a  series  of  dots 
he  made,  and  the  number  of  dots  shows  the  number  of 
I/rations  made  by  the  string. 


152  NATURAL    PHILOSOPHY. 

The  apparatus  by  which  the  paper  is  drawn  along 
is  not  shown  in  the  figure,  neither  is  that  by  which  time 
is  measured. 

With  this  apparatus  we  proceed  rapidly  to  verify  the 
laws  of  vibration. 

4.  The  first  law. — The  string  C  D,  was  taken  3  ft.  in 
length  :  stretched  by  a  weight  of  56  Ibs.  at  W,  it  made 
420  complete  or  double  vibrations  in  3  seconds.     The 
bridges,  C  and  D,  were  then  moved,  so  that  the  length 
of  the  string  was  4  ft.  ;  it  then  made  315  vibrations  in 
3  seconds.     But  420  is  to  315  as  4  :  3.     We  see  that 
when  the  lengths  of  the  string  are  as  3  :  4,  the  number 
of  vibrations  in  the  same  time  are  as  4  :  3.     Hence  the 
number  of  vibrations  in  a  given  time  varies  inversely 
as  the  lengths  of  the  string. 

5.  The  second  law. — The  string  was  again  made  4  ft. 
long,  and  the  weight  W,  56  Ibs.     The  vibrations  in  one 
second  then  numbered  1 05.    When  the  weight,  W,  was 
then  changed  to  14  Ibs.,  the  number  of  vibrations  in  one 
second  was,  in  some  experiments  52,  and  in  others  53. 
The  instrument  can  not  register  parts  of  a  vibration  ;  the 
true  number  is  evidently  between  52  and  53 ;  we  may 
call  it  52 \.     We  see  that  when  the  weights  are  56  and 
14,  or  as  4  :  1,  the  number  of  vibrations  made  in  a  second 
are  105  and  52|,  or  as  2  :  1.     Hence  the  number  of  vi- 
brations in  a  second,  varies  directly  as  the  square  root 
of  the  weight  by  which  the  string  is  stretched. 

6.  TJie  third  law.— The  string  which,  being  4  ft.  long, 
and  stretched  with  a  weight  of  56  Ibs.,  gave  105  vibra- 
tions a  second,  was  found  to  weigh  19.4  grs.  to  the  foot 
in  length.     Another  string,  weighing  43  grs.  to  the  foot, 
was  taken  of  the  same  length  and  tension  as  the  other, 
and  the  number  of  vibrations  in  one  second  was,  in 


NATURAL    PHILOSOIHY. 


153 


gome  experiments  70,  and  in  others  71.  The  true 
number  is  between  these;  call  it  70i.  Now,  the 
weight  of  equal  lengths  of  the  string  being  19.4 : 43, 
the  number  of  vibrations  are  found  to  be  105:70J-; 
but  105 :  70 2 : :  1/43 : 4/19^  so  nearly  that  we  may  infer, 
that  the  number  of  vibrations  a  second  varies  inversely 
as  the  square  root  of  the  weights  of  equal  lengths  of  the 
string.  [See  (107.)  6.] 

(47.)   In  progressive   vibra-  Fig.  n. 

tions,  the  motion  appears  to  be  L x\  '  / ^  \J 
lengthwise  of  the  cord.  A  cord 
may  divide  itself  into  parts, 
vibrating  separately,  called 
ventral  segments,  with  points 
of  rest  between  them,  called 
nodes. 

1.  Progressive  vibrations. — 
Let  a  heavy  cord,  or  better 
still,  an  india-rubber  tube  (A 
B,  Fig.  71),  several  feet  long, 
be  fastened  at  one  end  to 
the  wall  or  ceiling  of  the  room. 
Take  hold  of  the  other  end  with 
one  hand,  and  by  a  sudden  blow 
with  the  other,  push  the  part 
B  C  aside,  as  shown  in  the 
figure.  The  little  hillock  thus 
formed  will  run  swiftly  up  the 
tube  to  A,  and  then  quickly 
down  to  the  hand  again.  By 
carefully  noticing  the  motion, 
it  will  be  seen  that  while  the  hillock,  running  up  to  A 

7* 


151 


NATURAL    PHILOSOPHY. 


is  on  one  side  of  the  cord  or  tube,  that  which  returni 
Fi.  72.  to  the  hand  is  on  the  other.     Hav- 

ing gone  to  the  top,  as  seen  at  A',  it 
turns  as  seen  at  A",  and  then  comes 
down.  Nor  does  it  then  stop;  it 
will  again  and  again  run  up  and 
down  the  tube  until,  the  height  of 
the  hillock  growing  less  and  less, 
it  finally  disappears.  This  motion 
is  progressive  vibration. 

2.  The    motion   appears  to   be 
lengthwise  of  the  tube. — It  is  inter- 

°  esting  and  important  to  notice  that 
while  the  motion  appears  to  be 
lengthwise  of  the  cord  or  tube,  the 
only  real  motion  of  the  parts,  is 
back  and  forth,  across  their  first 
position. 

3.  Ventral  segments. — By  start- 
ing several  hillocks,  one  after  the 
other  quickly,  the  whole  cord  may 
be  thrown  into  a   series   of  hills- 
and  valleys,  as  shown  in  Fig.  72. 
In  this  case  the  motion  between  B 

and  D,  consisting  of  two  parts,  on  opposite  sides  of  the 
middle  line,  is  called  a  wave.  Two  waves  are  represented 
in  the  figure. 

By  skillfully  timing  the  impulses  of  the  hand,  the 
hillocks  on  both  sides  of  the  middle  line  in  Fig.  72, 
may  be  made  to  turn  themselves  over  at  the  same 
time.  In  that  case,  the  tube  will  present  the  appear 
ance  shown  in  Fig.  72  (B),  the  points  a  b  c,  being 
almost  stationary  while  the  parts  between  are  swing- 


NATURAL    PHILOSOPHY.  155 

ing  to  and  fro  across  the  middle  line,  making  vibra- 
tions, just  as  if  they  were  separate  cords. 

The  points  which  appear  to  be  at  rest  are  called 
nodes,  while  the  vibrating  parts  between  them,  are 
called  ventral  segments. 

(48.)  When  a  cord  fastened  at  both  ends  is  struck,  it 
vibrates  as  a  whole,  and  in  ventral  segments  at  the  same 
time. 

1.  It  vibrates  as  a  whole. — Suppose  the  cord  shown 
ji  Fig.  69,  to  be  struck  at  a  point  one-sixth  of  its  length 
from  the  end  5,  the  entire  cord  will  swing  back  and 
forth  just  as  represented  in  that  figure,  and  the  vibra- 
tion of  its  whole  length  will  be  governed  by  the  three 
laws  already  given,  in  (46). 

2.  Ventral  segments   at  the  same  time. — The   cord 
will  at  the  same  time  divide  itself  into  three  ventral 
segments,  each  of  which  will  make  a  series  of  separate 
vibrations,  while  taking  part  in  the  full  length  vibra- 
tion of  the  cord. 

Now,  as  each  segment  in  this  case  is  -J  the  length  of 
the  string,  it  must  (first  law)  vibrate  3  times  as  fast.  If 
the  string  is  struck  at  J of  its  length  from  the  end,  there 
will  be  2  segments,  each  -£-  as  long  as  the  string,  and  of 
course,  vibrating  2  times  as  fast. 

§  3.    OF   VIBRATIONS   JN   LIQUIDS   AND   GASES. 

(49.)  Progressive  vibrations  are- illustrated  by  water 
waves. 

Two  sets  of  water  waves  may  interfere  with  each 
other,  and  produce  a  single  set  different  from  either. 

1     Water  waves. — Let  a  pebble  be  tossed  into  the 


156  NATURAL    PHILOSOPHY. 

watei  of  a  lake  or  pond,  and  the  tranquil  surface  will 
be  carved  into  a  series  of  circular  ridges  and  furrows, 
which,  growing  gradually  larger  and  larger,  finally 
break  against  the  shore.  The  motion  appears  to  be  in 
all  directions  outward  from  the  pebble,  but  the  little 
sticks  and  straws  that  may  be  resting  upon  the  water 
at  the  time,  tell  us,  by  their  dancing,  that  the  real  mo- 
tion of  the  water  is,  like  their  own,  a  motion  only  up 
and  down. 

A  wave  of  water  consists  of  two  parts,  a  ridge  and  a 
furrow. 

2.  Water  waves  may  interfere. — Let  two  sets  of 
water  waves  be  started  at  the  same  time,  by  dropping 
two  pebbles  at  a  little  distance  from  each  other.  The 
two  sets  of  growing  circles  very  soon  cross  each  other, 
and  then  the  smooth  surface  of  the  water  will  be  cut  up 
into  a  curious  confusion  of  dancing  hummocks.  Some 
of  these  hummocks  will  be  twice  as  high  as  the  ridges 
of  either  set  of  waves,  while  others  will  just  lift  their 
heads  above  the  original  surface  of  the  water.  When 
two  sets  of  waves  are  thrown  together,  they  are  said  to 
interfere. 

But  why  are  the  hummocks  of  such  different  heights  ? 
It  is  clear  that  when  two  ridges  come  together  their 
heights  will  be  united,  and  the  height  of  the  hummock 
will  be  the  sum  of  their  separate  heights.  But  when 
the  ridges  of  one  set  enter  the  furrows  of  the  other,  the 
height  of  the  resulting  hummock  will  be  equal  to  their 
difference.  Now,  as  the  waves  are  running  across  each 
other,  the  hummocks  must  be  of  various  heights, 
limited  on  the  one  hand  by  the  sum,  and  on  the  other, 
by  the  difference  in  the  heights  of  the  ridges  of  the  two 
nets. 





NATURAL    PHILOSOPHY.  157 

(50.)  The  vibrations  of  air  consist  of  alternate  rare- 
factions   and  condensations.      In   free  air  the   waves 
travel  outward  from  their  source  in  every  possible  di 
rection.     Different  sets  must  be  constantly  interfering. 

1.  Alternate  rarefactions  and  condensations. — "We 
have  seen  [see  (16.)  1  and  2]  how  easily  air  may  be 
compressed,  and  with  what  promptness  it  springs  back 
to  its  former  volume  when  the  compressing  force  is  re- 
moved. Now,  suppose  that  near  to  one  end  of  a  long 
tube,  is  a  piston  P  (Fig.  73).  By  suddenly  rig.  7a 
pushing  this  piston  forward  to  P',  and  then 
instantly  pulling  it  back,  the  air  in  the  whole 
length  of  the  tube  will  be  put  in  motion. 
Let  us  analyze  this  motion. 

When  the  piston  moves  from  P,  it  crowds 
the  air  before  it,  and  when  it  has  reached  P', 
this  crowding  effect  will  have  gone  forward 
to  some  point  A,  more  or  less  distant.  The 
space,  P'  A,  is  then  filled  with  condensed 
air.  E"ow,  when  the  pressure  of  the  piston 
is  removed,  the  condensed  air  springs  back. 
It  springs  both  ways,  backward  against  the 
piston  and  forward  against  the  air  at  A. 
By  its  pressure  against  the  air  at  A,  the  air 
in  the  space  A  B,  will  be  condensed.  The 
next  moment  this  air  expands,  and  pressing 
both  ways,  condenses  the  air  B  C,  in  front 
of  it  and  also  the  air  A  P,  behind  it.  These 
two  portions  will,  in  this  way,  be  condensed, 
while  the  air,  A  B,  will  be  rarefied.  The 
next  instant  these  condensed  portions  spring  back  and 
become  rarefied,  while  the  rarefied  portion  A  B,  and  at 


158  NATURAL    PHILOSOPHY. 

the  same  time,  another  part  beyond  C,  will  be  condensed. 
The  air  is  in  this  way  thrown  into  a  series  of  condensed 
and  rarefied  parts,  alternately  springing  back  and  forth 
in  the  direction  lengthwise  of  the  tube.  We  need  only 
add,  that  there  is  no  sudden  transition  from  condensed 
to  rarefied  air  at  the  points  A  B  and  C.  The  mobility 
of  air  will  not  permit  this.  At  the  middle  of  the  con- 
densed part  the  condensation  is  greatest,  while  at  the 
middle  of  the  rarefied  part  is  the  greatest  rarefaction, 
and  between  these  points  the  change  is  gradual. 

A  wave  of  air  consists  of  two  parts,  a  condensation 
and  a  rarefaction, 

2.  Waves  in  free  air  go  in  all  directions. — The  walls 
of  the  tube  confine  the  air,  and  compel  its  waves 
to  go  in  the  direction  of  its  length ;  in  free  air  the  case 
is  different.  Every  impulse  by  which  the  atmosphere 
at  any  point  is  suddenly  condensed  or  rarefied,  is  the 
center  from  which  air  waves  go  outward  in  all  direc- 
tions. 

Let  a  few  grains  of  gunpowder  be  exploded.  A  little 
sphere  of  air  at  the  point  where  the  explosion  occurs, 
will  be,  for  the  moment,  rarefied,  while  by  its  pressure 
a  shell  of  air  outside  of  it  will  be  condensed.  This 
condensed  air  instantly  springing  back,  condenses  the 
air  on  both  sides  of  it,  and  itself  becomes  rarefied, 
The  waves  will  thus  travel  outward  from  the  center, 
antil  the  whole  body  of  air  is  thrown  into  a  series  of 
concentric  shells,  alternately  condensed  and  rarefied. 

How  constant  and  complicated  must  be  these  vibra- 
tions of  the  air !  Every  sudden  and  local  puff  of  wind ; 
every  forcible  breath  exhaled  from  the  lungs ;  the  fall 
of  every  stick  and  stone,  all  these  are  the  sources  of  ai 
many  different  sets  of  waves  spreading  in  all  directions, 


NATURAL    PHILOSOPHY.  159 

darting  across  and  through  each  other,  too  delicate  to 
be  seen  or  felt,  presenting  to  the  mind  a  scene  of  activ- 
ity far  exceeding  the  power  of  the  senses  to  appreciate. 
3.  Different  sets  interfere. — Suppose  two  sets  of'  air 
waves  come  together ;  if  their  condensed  parts  coincide, 
a  single  set  will  be  formed  whose  condensations  are 
greater  than  either.  If  the  condensed  parts  of  one  set 
coincide  with  the  rarefied  parts  of  the  other,  there  will 
be  a  single  set  whose  condensations  are  less  than  either. 
In  the  first  case,  if  the  two  sets  are  equal,  the  resulting 
waves  will  be  doubled ;  if,  in  the  other  case,  the  two  sets 
are  equal,  they  will  destroy  each  other,  leaving  the  air 
without  waves. 

§   4.     OF    THE     VIBRATIONS    OF    MOLECULES. 

(51.)  The  molecules  of  all  bodies  are  at  all  times  in 
motion.  These  vibrations  of  molecules  can  not  be  seen, 
yet  they  are  able  to  affect  our  senses.  Acting  upon  the 
ear  they  produce  sound;  upon  the  eye  they  are  recog- 
nized as  light;  while  upon  the  sense  of  touch  they  pro- 
duce heat. 

1.  Molecules  in  motion. — The  molecules  of  bodies  do 
not  touch  each  other  ;  if  they  did,  they  could  never  be 
pushed  nearer  together,  and  there  could  be  no  such 
thing  as  elasticity.  They  are  distinct,  separate  bodies. 
Moreover,  they  are  supposed  to  be  in  rapid  motion. 
lust  how  they  move  is  not  known.  They  may  be 
swinging  back  and  forth  in  straight  lines,  or  in  curves ; 
they  may  be  rolling  on  their  axes  to  and  fro,  or  perhaps 
revolving  around  each  other :  or  it  may  be  that  they 
make  several  of  these  motions  at  once.  Be  this  as  it 
may,  they  are  supposed  to  be  in  motion  of  some  kind. 


160  NATURAL     PHILOSOPHY. 

The  vibrations  of  the  molecules  may  be  increased  or 
diminished.  To  illustrate :  look  upon  a  bar  of  iron  ; 
imagine  the  multitude  of  little  molecules  of  which  it  is 
made  ;  see  them  in  rapid  vibration,  trembling  in  their 
little  spaces.  Now  strike  the  bar  with  a  hammer ;  the 
hammer  can  not  stop  without  giving  the  force  which 
moves  it,  to  the  molecules  of  the  bar,  and  every  mole- 
cule acted  on  by  this  force,  has  its  vibrations  thereby 
quickened. 

2.  These  vibrations  affect  the  senses. — The  motions  of 
the  molecules  are  quite  too  delicate  to  be  seen.  They 
are  supposed  to  exist,  only  because  many  effects  can 
be  explained  in  no  other  way  so  well  as  on  this  suppo- 
sition. They  are  thought  to  be  the  means  by  which 
objects  of  matter  produce  effects  on  our  senses.  The 
organs  of  sense  are  so  arranged  by  Him  who  made  them, 
that  each  one  receives  a  different  effect,  although  the 
vibrations  that  produce  it  may  in  all  cases  be  much 
alike.  The  ear  is  so  made  that  vibrations  in  it  produce 
sound.  The  eye  is  so  made  that  vibrations  are  recog- 
nized as  light.  The  sense  of  touch  is  so  arranged  that 
vibrations  against  it  are  felt  as  heat.  The  phenomena 
of  sound  and  light  and  heat  are  caused  by  vibrations. 
How  simple  the  means  to  produce  such  wonderful  re- 
sults I  "  Know  ye,  that  the  Lord  he  is  God ;  it  is  li« 
that  hath  made  us,  and  not  we  ourselves  1" 


NATURAL    PHILOSOPHY.  161 


CHAPTEE   V. 


MODES  OF  VIBRATION.— L   SOUND. 

§    1.   THE   ORIGIN   AND  THE   TRANSMISSION   OF   SOUND. 

(52.)  READ  (51).  Sound  is  a  sensation  produced  in  tho 
ear  by  the  vibrations  of  external  bodies. 

1.  Sound  produced  ly  vibrations. — Let  two  books  be 
clapped  together,  and  every  ear  in  the  room  receives  a 
shock,  to  which  the  name  of  sound  is  given.  The  mole- 
cules of  the  books  are  made  to  vibrate  by  the  blow,  and 
these  vibrations,  acting  upon  the  air  in  contact  with 
them,  produce  air  waves.  These  air  waves,  traveling 
outward  in  all  directions,  finally  reach  the  ear,  and  the 
many  parts  of  this  organ  receiving  these  vibrations,  en- 
able the  mind  to  recognize  the  peculiar  sensation  which 
we  call  sound. 

When  we  listen  to  the  sound  of  a  church  bell,  we 
may  in  like  manner  imagine  the  molecules  of  the  bell 
all  in  a  state  of  tremulous  motion,  caused  by  the  blowa 
of  the  hammer.  This  motion  causes  vibration  in  the 
air  in  contact  with  the  bell.  The  air  waves  thus  formed, 
travel  in  all  directions  from  the  bell  until  the  ear  re- 
ceives them. 

The  roar  of  a  cataract  is  the  result  of  vibrationa 
caused  by  the  falling  water.  The  rolling  soand  of 


NATURAL    PHILOSOPHY. 

thunder  is  the  effect  of  vibrations  in  air,  caused  by 
electricity.  Every  sound  in  nature,  or  that  can  be  pro- 
duced by  art,  may  be  traced  back  through  the  waves 
of  some  medium,  to  the  vibrating  molecules  of  some 
solid,  liquid,  or  gaseous  body. 

(53.)  Sound  waves  travel  through  all  elastic  media 
or  bodies.  The  velocity  of  sound  is  not  the  same  in  dif- 
ferent substances  ;  it  is  governed  by  two  laws  : — 

1st.  The  velocity  of  sound  varies  inversely  as  the 
square  root  of  the  density  of  the  substance. 

2d.  The  velocity  of  sound  varies  directly  as  the  square 
root  of  the  elasticity  of  the  substance. 

In  the  same  medium,  the  velocity  of  sound  is  uniform. 

1.  Sound  waves. — All  sounds  are  the  effects  of  vibra- 
tions, but  it  is  not  true  that  all  vibrations  produce 
sound.  There  are  vibrations  too  slow  to  affect  the  ear ; 
such  are  the  vibrations  of  a  cord  not  over-stretched.  On 
the  other  hand,  there  are  vibrations  which  are  too  rapid 
to  be  heard.  The  lower  limit  has  been  fixed  at  16  vi- 
brations a  second,  and  the  higher  at  38,000.  Waves 
which  occur  within  these  limits  of  velocity  can  be  heard, 
and  are  called  sound  waves. 

It  is  interesting  to  notice  that  the  limits  of  hearing 
are  not  the  same  in  all  persons.  "  Nothing  can  be 
more  surprising  than  to  see  two  persons,  neither  of 
them  deaf,  the  one  complaining  of  the  penetrating 
elirjllness  of  a  sound,  while  the  other  maintains  that 
there  Li  no  sound  at  all."  "  In  the  'Glaciers  of  the 
Alps  '  I  have  referred  to  a  case  of  short  auditory  range 
noticed  by  myself  in  crossing  the  Wengern  Alp  in  com- 
pany with  a  friend.  The  grass  at  each  side  of  the  path 
swarmed  with  insects  which,  to  me,  rent  the  air  with 


NATURAL    PHILOSOPHY.  163 

their  shrill  chirruping.  My  friend  heard  no  tiling  of 
this,  the  insect  music  lying  quite  beyond  his  range  of 
audition."  (See  Tyndall's  Lect.  on  Sound.) 

2.  Are  transmitted  through  all  elastic  bodies. — NU 
merous  facts    easily   verified,   prove    this    statement. 
When,  for  example,  the  blows  of  a  hammer  fall  upon 
one  end  of  a  long  wooden  beam,  an  ear  placed  in  con- 
tact with  the  other  end  hears  the  sound  with  surprising 
distinctness.     The  same  thing  is  true  of  other  solid 
bodies.     The  clatter  of  horses'  hoofs,  or  the  rattle  of  a 
railway  train,  quite  inaudible  to  one  who  stands  erect, 
is  heard  distinctly  when  the  ear  is  placed  in  contact 
with  the  ground.     The  solid  earth  transmits  the  sound 
waves. 

In  liquids,  also,  sound  waves  travel  freely.  Let  two 
stones  be  struck  together  under  water ;  the  sound  will 
be  heard  by  an  ear,  itself  under  water,  a  long  distance 
away. 

The  transmission  of  sound  waves  through  gases  is 
sufficiently  familiar ;  the  sounds  which  throng  the  ear 
BO  constantly  are  transmitted  through  the  atmosphere. 

3.  The  velocity  not  the  same  in  all  media. — The  ve- 
locity of  sound  in  a  great  many  substances,  has  been 
found  by  laborious  and  skillful  experiments  (see  Tyn- 
dall's Lect.  on  Sound,  p.  26).     In  the  following  table 
some  of  these  results  are  collected  : — 


SUBSTANCES. 

TEMPEUATUF.E. 

VBLOCCTT. 

Air  

32  °F. 

1  092  ft. 

Air   ... 

61    " 

1  118  " 

Osyuren  .  . 

32    " 

1  040  " 

32    " 

4,164  " 

River  Water    

69    " 

4714  " 

Iron  

68    " 

16822  " 

Pine  Wood  

10,900  " 

164  NATURAL    PHILOSOPHY. 

The  velocity  of  sound  depends  upon  the  density  and 
the  elasticity  of  the  medium  in  which  it  travels. 

4.  The  first  law. — The  density  of  oxygen,  other  tilings 
being  equal,  is  about  16  times  that  of  hydrogen.     But 
we  see  in  the  table  that  the  velocity  of  sound  in  oxygen, 
is  only  about  J  as  great  as  in  hydrogen.     In  this  case 
the  velocity  is  in  versely  as  the  square  root  of  the  density 
of  the  medium.     This  law  may  be  verified  by  repeated 
experiments. 

5.  The  second  law. — When  air  is  heated  in  a  tight 
vessel  its  elasticity  is  increased,  while  its  density  is  un- 
changed.    In  this  condition  it  will  conduct  sound  more 
rapidly.     If  the  elasticity  of  air  be  made  4  times  as 
great,  the   velocity  of  sound   will   be   doubled.     The 
velocity  of  sound  in  this  case  is  directly  as  the  square 
root  of  the  elasticity  of  the  medium.     It  is  so  in  all 
cases. 

It  is  evident  that  both  density  and  elasticity  must  be 
known,  before  we  can  judge  the  power  of  a  substance  to 
conduct  sound.  Liquids  are,  for  example,  more  dense 
than  gases :  their  conducting  power,  on  this  account, 
would  be  less ;  but  on  the  other  hand  their  elasticity 
measured  ~by  the  force  required  to  compress  them  is 
vastly  greater,  so  that,  as  the  table  shows,  water  con- 
ducts sound  better  than  air. 

6.  But  in  the  same  medium  velocity  is  uniform. — 
The  velocity  of  sound  waves  in  air  or  in  water,  for  ex- 
ample, is  uniform.     Moreover,  all  sounds  in  the  same 
medium   travel   with   the   same   velocity.     When  we 
listen  to  the  music  of  a  distant  band,  the  various  notes, 
high  and  low,  loud  and  soft,  reach  the  ear  in  the  same 
order  in  which  they  were  made.     So  also   the  shrill 
chirping  of  insects,  the  dull  thud  of  a  falling  stone,  the 


NATURAL    PHILOSOPHY.  165 

melodious  songs  of  the  birds,  and  the  murmur  of  rivulets, 
are  all  borne  with  equal  swiftness  through  the  air. 

So  uniform  is  the  velocity  of  sound,  that  distances 
may  be  measured  by  means  of  it.  Suppose  the  flash  ol 
a  cannon  on  a  distant  hill  was  seen,  and  in  10  seconds 
afterward  the  report  was  heard,  the  temperature  at  the 
time  being  61°  F.  The  velocity  of  sound  is  1,118  ft. 
and  the  sound  waves,  starting  when  the  flash  was  seen, 
took  ten  seconds  to  reach  the  ear.  1,118  x  10=11,180. 
The  observer  was  at  distance  of  11,180ft.  from  the 
cannon. 

§   2.    OF  KEFEACTION   AND   REFLECTION   OF   SOUND. 

(54.)  Sound  waves  will  pass  from  one  medium  to 
another.  In  this  case  refraction  of  sound  occurs. 
Sound  may  be  made  louder,  by  so  refracting  the  waves 
that  they  will  be  collected  at  the  p]  ace  where  the  sound 
is  heard. 

1.  Sound  waves  pass  from  one  medium  to  another. — 
When  in  a  room,  with  doors  and  windows .  closed,  we 
are  able  to  hear  sounds  distinctly  that  are  made  in  the 
open  air.      The  rattling  of  carriages,  the  singing  of 
birds,  and  the  voices  of  friends,  come  freely  through 
the  solid  walls  of  our  houses.     To  do  this,  the  sound 
waves  must  pass  from  the  air  outside,  into  the  solid 
material  of  the  wall,  and  then  from  this  again  into  the 
air  of  the  room. 

2.  Refraction  of  sound. — Now,  when  sound  waves 
go  from  one  medium  into  another,  they  are  bent  out  of 
the  straight  line  in  which  they  were  moving ;  this  ia 
tailed  refraction  of  sound. 


166  NATURAL    PHILOSOPHY. 

To  illustrate  retraction  :  Suppose  the  lines  B  C  and  P 
B.  (Fig.  74)  to  represent  two  sound  waves  passing  through 
Fig.  74  air  and  striking  the  sur- 

face of  another  substance 
A  A,  at  the  points  C  and 
H.  They  will  not  go 
through  in  straight  lines 
to  E  and  L,  but  on  enter- 
ing the  denser  medium 
A  A,  they  will  be  bent 
taking  the  direction  C  D 
and  H  K,  and  when  they 
emerge  they  will  be 
ag-ain  bent,  so  as  to  take  the  direction  D  E  and  K  L.  In 
this  case,  the  refracted  waves  D  E  and  K  L  are  paral- 
lel to  the  original  waves  B  C  and  F  H.  It  will  always 
be  so  when  the  sides  of  the  medium,  A  A,  are  plane 
and  parallel. 

3.  Sound  made  louder  ~by  refraction. — If  the  surfaces 
of  the  medium  are  curved  instead  of  being  plane  and 
parallel,  the  sound  waves  which  pass  through  will  not 
come  out  parallel  to  those  which  enter.  It  may  be  that 
the  waves  which  enter  are  separating  from  each  other, 
and  yet  those  that  come  out  are  approaching  each  other. 
In  this  way  sound  waves  may  be  collected  at  a  point,  so 
that  a  sound  may  be  heard  there,  which  would  not  oth- 
erwise be  audible. 

This  interesting  fact  may  be  illustrated  by  a  cu- 
rious experiment.  A  sack  a  m  n  (Fig.  75),  made  of 
twc  films  of  col^dion,  or  of  very  thin  india-rubber, 
united  at  their  edges  by  a  rim  of  iron,  is  filled  with  car- 
bonic acid — a  gas  much  denser  than  air.  A  watch  ia 
placed  at  "W,  near  to  the  sack.  If  now  a  person  put  his 


NATURAL    PHILOSOPHY. 

ear  at  S,  it  may  be,  a  point  at  a  distance  of  five  or  six 
feet  on  the  other  side  of  the  sack,  the  ticking  of  the 
watch  will  be  heard  distinctly.  If  the  ear  be  moved 


Fig.  75. 


from  this  place  ever  so  little,  the  sound  will  be  more 
feeble,  and  if  the  sack  be  taken  away  the  sound  will 
not  be  heard  at  all. 

This  experiment  beautifully,  illustrates  refraction. 
The  sound  waves  which  start  from  the  watch  would  go 
in  straight  lines  outward,  farther  and  farther  apart.  .  But 
they  strike  the  surface  of  the  sack  at  points  a  in, 
&c. ;  pass  into  it  and  through  it,  being  bent  from  their 
course  so  as  to  emerge  in  the  directions  which  take 
them  all  to  the  point  S.  So  many  vibrations  are  thus 
collected  at  this  point  that  the  sound  is  heard,  whereas, 
if  the  sack  were  taken  away,  they  would  be  so  scattered 
that  no  sound  would  be  produced. 

v  (55.)  "When  sound  waves  fall  upon  the  surface  of  a 
second  medium,  only  a  part  of  them  enter ;  the  rest  are 
reflected.  The  reflection  of  sound  is  governed  by  the 
following  law : — 


1C8  NATURAL    PHILOSOPHY. 

The  angle  of  reflection  must  be  equal  to  the  angle  of 
incidence. 
An  echo  is  produced  by  the  reflection  of  sound. 

1.  The  reflection  of  sound. — To  illustrate  the  reflec- 

tion of  sound  suppose  the  line  I  A 
rtg.  76.  (Fig.  76)  to  represent  the  direction 

of  several  sound  waves,  which,  pass- 
ing through  the  air,  strike  a  body 
M  M.  Some  of  tliese  waves  will 
pass  through  the  body,  being  re- 
fracted, but  others  will  be  thrown 
off  in  the  direction  A  R.  These 
are  the  reflected  waves. 

Now,  a  person  standing  at  R 
will  hear  the  voice  of  another  at  I,  when  the  distance 
is  considerable,  sounding  as  though  it  came  from  a 
person  in  the  direction  R  A.  We  always  judge  the 
direction  of  a  sounding  body  from  us,  to  be  that  from 
which  the  waves  enter  the  ear. 

2.  The  law  of  reflection. — To  understand  the  language 
of  this  law,  let  us  refer  again  to  Fig.  76.     The  waves  I 
A,  those  which  fall   upon   the  reflecting  surface,  are 
called  the  incident  waves :  the  waves  A  R,  those  that 
are  thrown  off  from  the  surface,  are  called  the  reflected 
waves,  and  the  point,  A,  is  called  the  point  of  incidence. 
Now,  if  a  perpendicular  A  P,  be  drawn  to  the  reflect 
ing  surface  at  the  point  of  incidence,  then  the  angle  I 
A  P,  is  the  angle  of  incidence,  and  the  angle  PAR, 
is  the  angle  of  reflection.     The  law  of  reflection  re- 
quires that  these  angles  shall  always  be  equal. 

3.  The  echo. — An  echo  is  a  repetition  of  sound  pro- 
duced by  the  reflection  of  waves  from  a  distant  object. 
Who,  after  loudly  uttering  a  word  or  sentence,  has  not 


NATURAL    PHILOSOPHY.  169 

sometimes  listened  to  the  sound  of  his  own  voice  coming 
back  to  him  from  a  distant  wood,  or  from  the  face  of  a 
cliff;  or,  it  may  be,  from  the  wall  of  a  distant  building  ? 
Visitors  to  Cooperstown  will  not  soon  forget  the  fine 
echo  returned  from  the  rocky  hills  which  skirt  Otse- 
go  Lake.  There,  we  are  told  by  Fennimore  Cooper, 
once  dwelt  Natta  Burnpo,  the  hero  in  the  story  of  the 
''Pioneers."  Let  his  name  be  loudly  called  from  a  cer 
tain  place  upon  the  lake,  and  immediately  the  response — 
Nat-ta-Bum-po,  every  syllable  full  and  clear,  rings  back 
over  the  water  as  if  spoken  by  the  hero  himself  from  hi? 
cave  in  the  cliffs. 

When  two  obstacles  are  opposite  to  one  another,  the 
sound  may  be  reflected  back  and  forth  many  times. 
Surprising  repetitions  of  echoes  are,  in  this  way,  some- 
times produced.  It  is  said  that  an  echo  near  Milan 
repeats  a  single  sound  thirty  times.  "  When  a  trumpet 
is  sounded  at  the  proper  place  in  the  Gap  of  Dunloe, 
the  sonorous  waves  reach  the  ear  after  one,  two,  three, 
or  more  reflections  from  the  adjacent  cliffs,  and  thus 
die  away  in  the  sweetest  cadences." 

§  3.    ON    MUSICAL    SOUNDS. 

(56.)  Musical  sounds  are  caused  by  rapid  vibrations 
which  follow  each  other  with  great  regularity.  Any 
noise  whatever,  when  repeated  rapidly,  will  cause  a 
continuous  tone :  even  separate  puffs  of  air,  following 
each  other  rapidly,  produce  a  music&l  sound. 

1.  Musical  sounds. — When  a  single  and  intense  air 

wave  is  suddenly  produced,  as  when  a  gun  is  tired,  the 

resulting  sound  is  called  a  report.     Let  a  series  of  such 

sounds  be  made  in  quick  but  irregular  succession,  and 

I 


1TO 


NATURAL    PHILOSOPHY. 


the  resulting  sound  is  called  uoise.  But  when  the 
waves  are  made  with  regularity,  and  follow  each  other 
so  swiftly  that  the  ear  can  dir/t'nguish  no  interval  of 
time  between  them,  the  result  in  a  musical  sound. 

2,.  Any  noise  repeated  rapidly  causes  a  continuous 
tone. — [No  matter  what  the  source  of  the  wares  may 
be,  nor  how  unmusical  the  separate  noises,  only  let 
them  be  repeated  with  regularity  and  rapidity,  and 
they  will  result  in  music.  Slowly  pass  a  piece  of  ivory, 
or  even  the  finger  nail,  over  the  rough  surface  of  a 
wound  piano  wire,  and  the  sovmd  of  its  strokes  against 
the  separate  ridges  is  altogether  unpleasant ;  but  pass  it 
quickly  over  the  same  surface,  and  the  ear  is  saluted 
with  a  musical  tone  of  surprising  shrillness  and  purity. 
If  a  card  be  pressed  against  the  teeth  of  a  wheel  which 
rotates  slowly,  a  series  of  distinct  and  unpleasant  taps 
.will  be  heard;  but,  if  by  means  of  a  larger  wheel  and 
band,  this  wheel  be  made  to  revolve  rapidly,  the  taps 
will  coalesce  and  salute  the  ear  with  music. 

3.  Puffs  of  air  made  rapidly 
produce  a  musical  sound. — The 
syren  is  an  instrument  by  which 
a  series  of  air  puffs  are  made  to 
produce  a  musical  sound,  and 
by  which  the  number  of  puffs 
made  in  a  second  are  registered. 
Its  structure  may  be  learned 
from  Fig.  77. 

A  brass  tube  O,  leads  from 
a  wind  chest  E,  to  a  brass  plate, 
a  by  which  is  pierced  with  a 
series  of  holes  arranged  around 
the  circumference  of  a  circle. 


Fig.  77. 


NATURAL    PHILOSOPHY.  17; 

Above  this  plate  is  a  disk  c  d,  also  perforated  with 
holes  exactly  corresponding  to  those  in  the  plate  below. 
The  disk  is  provided  with  a  steel  axis  A,  and  is  so 
fixed  that  it  may  rotate  with  a  very  small  amount  of 
friction.  The  wheel  work  shown  in  the  upper  part  of 
the  figure  registers  the  number  of  puffs  made  in  any 
given  time. 

Now,  when  the  disk  c  d  revolves,  the  holes  in  it  will 
be  brought  alternately  over  the  perforations  in  the  plate 
a  5,  and  the  spaces  between  them,  so  that  these  holes 
will  be  alternately  opened  and  closed.  When  the  disk 
is  still,  and  the  holes  are  open,  if  air  be  urged  through 
the?  tube  O,  it  will  escape  from  the  top  in  steady 
streams,  but  when  the  disk  revolves  these  streams  will 
be  cut  up  into  successive  puffs.  If  the  disk  turns 
slowly,  the  separate  puffs  are  heard,  but  as  the  disk  is 
turned  more  and  more  rapidly,  the  air  announces  its 
escape  by  a  musical  sound  of  great  purity  and  increas- 
ing shrillness. 

By  a  simple  artifice,  the  air  which  gives  the  sound 
is  made  to  turn  the  disk.  This  is  done  by  making  the 
holes  through  the  plate  a  I,  oblique  instead  of  vertical ; 
those  in  the  disk  being  also  oblique,  but  inclined  in  the 
opposite  direction. 

(57.)  Musical  sounds  differ  in  three  respects :  1st, 
Pitch ;  2d,  Intensity ;  and  3d,  Quality. 

i. — PITCH. 

A. — Pitch  depends  entirely  upon  the  rapidity  of 
vibrations  which  produce  the  sound. 

The  difference  in  the  pitch  of  two  sounds,  is  called 
an  interval,  and  a  series  of  eight  sounds  of  different 


172  NATURAL    PHILOSOPHY. 

pitch,  lias  been  adopted  as  the  foundation  of  all 
music,  and  called  the  diatonic  scale.  The  number  of 
vibrations  to  produce  the  note  a  of  the  treble  clef,  is  440 
a  second. 

1.  Pitch  depends  on   the  rapidity  of  vibration, — 
The  pitch  of  sounds  is  that  which  distinguishes  them 
as  being  high  or  low.     It  depends  entirely  upon  the 
-apidity  of  vibration :  tl  e  more  rapid  the  vibrations,  the 
iiigher  will  be  the  sound  produced.     Two  sounds  made 
by  the  same  number  of  vibrations  per  second,  however 
much  they  may  differ  in  other  respects,  will  have  the 
Bame  pitch. 

2.  Intervals. — When  the  number  of  vibrations  which 
produce  one  sound,  is  twice  as  great  as  that  which  pro- 
duces another,  we  must  not  say  that  the  sound  is  twice 
an  high,  but  rather  that  it  is  an  octave  above.     The  term 
octave,  is  used  to  designate  a  tone  which  is  made  by 
twice  the  number  of  vibrations  needed  to  produce  a 
lower  one,  called  the  fundamental.      Other  intervals 
will  be  named  in  the  description  of  the  scale. 

3f.  The  diatonic  scale. — Now  the  difference  in  pitch, 
or  the  interval  between  a  fundamental  note  and  its 
octave,  is  very  great.  To  fill  up  this  interval,  sounds 
have  been  chosen  which  blend,  or  harmonize  most  per- 
fectly with  the  fundamental,  or  with  each  other.  These, 
placed  between  the  fundamental  and  its  octave,  form 
a  series  of  eight  notes,  called  the  natural,  or  the  diatonic 
scale. 

The  eight  notes  of  the  scale  are  expressed  by  the 
following  names  and  intervals  : — 

Names,        C,    D,    E,    F,    G,    A,    B,    C. 

Intervals,    1st,  2d,  3d,  4th,  5th,  6th,  7th,  8th. 


NATURAL    PHILOSOPHY.  173 

Tliis  scale  repeated  about  eleven  times,  making 
what  is  termed  in  music  eleven  octaves,  will  include  all 
Bounds  within  the  range  of  the  human  ear.  Only  about 
seven  octaves  are  available  in  music. 

The  method  of  representing  the  notes  in  music  is 
familiar  to  all.  Remember  that  the  note  called  A,  is 
found  in  the  second  space  of  the  treble  clef,  and  the 
position  of  all  others  may  be  easily  traced. 

4.  Number  of  vibrations  for  the  notes. — The  num- 
ber of  vibrations  to  produce  the  various  notes,  may  be 
found  by  experiment  with  the  syren.  (See  Tyndall  on 
Sound.)  It  has  been  found  that  the  note  A,  of  the 
treble  clef  is  made  by  440  vibrations  a  second.  (See 
Silliman's  Phys.)  In  piano-fortes  for  private  use,  this 
note  is  produced  by  about  420  vibrations  a  second. 

If  we  represent  the  number  of  vibrations  for  the 
fundamental  note  by  1 ,  then  the  several  notes  of  the 
scale  will  be  made  by  the  following  ratios : — 

C,    D,    E,    F,    G,    A,    B,    C. 
1,    I,     t,    t,    I,     i    V,    2. 

Now,  remembering  this  series  of  fractions,  and  the  fact 
that  A  is  made  by  440,  the  number  of  vibrations  for 
all  the  others  may  be  found.  Thus  for  example,  how 
many  vibrations  to  give  the  fundamental  C  ?  The  rel- 
ative number  of  vibrations  for  A  and  C  are  -|  and  1 ; 
that  is,  A  is  produced  by  |  as  many  vibrations  as  C  ; 
or,  to  reverse  the  ratio,  C  requires  f  as  many  as  A,  and 
|  x  440=264.  Having  this  number  for  the  fundament- 
al, multiply  this  by  the  fractions  -f,  |>  f ,  &c.,  and  the 
numbers  for  the  corresponding  notes  will  be  obtained. 
These  multiplied  by  2  will  give  the  number  for  the 
notes  in  the  next  higher  octave,  or  divided  by  2, 


174  NATURAL    PHILOSOPHY. 

will  give  the  numbers  for  the  notes  in  the  octare 
below. 

n. — INTENSITY. 

B  — The  intensity  of  sound  is  that  which  distinguish- 
es it  as  being  loud  or  soft.  It  depends  entirely  upon 
the  amplitude  of  the  vibrations  which  produce  it.  The 
greater  the  amplitude,  the  louder  the  sound  will  ba  In 
the  case  of  a  vibrating  string  for  example,  the  loudness 
or  intensity  of  the  sound  made  by  it,  will  depend  en- 
tirely upon  the  distance  through  which  the  string  vi- 
brates across  its  line  of  rest. 

m. — QUALITY. 

C. — By  quality,  we  refer  to  that  peculiarity  of  sound 
by  which  we  may  distinguish  notes  of  the  same  pitch 
and  intensity,  made  on  different  instruments.  The 
pitch  and  intensity  of  notes  made  on  a  violin  and  on  a 
piano  may  not  differ,  and  yet  how  easy  to  tell  the  sounds 
apart.  We  recognize  the  voices  of  friends,  not  by  their 
pitch  nor  their  intensity,  but  by  their  quality. 

Quality  is  thought  to  depend  upon  the  different  sets 
of  vibration,  which,  in  different  instruments,  combine 
with  those  that  cause  the  leading  tone.  The  material 
of  a  violin  vibrates  as  well  as  the  string  which  is  stretched 
upon  it,  and  the  sound  made  by  both  sets  of  vibrations 
is  the  real  tone  of  the  instrument.  The  various  parts 
of  a  piano  vibrate  as  well  as  the  piano  wire,  and  the 
sound  produced  by  all  these  vibrations  together  is  the 
familiar  sound  of  the  instrument.  Now,  it  is  clear  that 
the  sets  of  vibration  in  these  two  instruments  must  be 
different,  and  for  this  cause  the  quality  of  tho  two 
tones  is  different. 


NATURAL     PHILOSOPHY.  175 

(58.)  Musical  instruments  are,  for  the  most  part,  of 
two  classes :  first,  those  in  which  the  sounds  are  pro- 
duced by  vibrating  strings,  and,  second,  those  in  which 
sounds  are  made  by  vibrating  columns  of  air 

Y 

I. STRINGED    INSTRUMENTS. 

A. — In  stringed  instruments,  the  pitch  of  the  different 
notes  is  obtained  by  using  strings  or  wires  of  different 
lengths,  of  different  tensions,  and  of  different  weights. 

1.  Stringed  instruments. — The  violin,  the  guitar,  and 
the  piano,  are  familiar  forms  of  stringed  instruments. 
In  every  case,  cords  or  wires  are  tightly  stretched  over 
some  solid  body  having  considerable  surface.    The  music 
of  these  instruments  is  not  made  by  the  vibrations  of 
their  cords  alone ;  the  simple  vibration  of  a  cord  is  not 
able  to  produce  sound  of  sufficient  intensity,  but  by 
being  stretched  over  hollow  boxes  made  of  elastic  wood, 
the  material  of  the  box,  and  the  air  inside  of  it  are 
made  to  vibrate,  and  these  vibrations,  joined  with  those 
of  the  cords,  produce  the  sounds  of  the  instrument. 

2.  Pitch  varied  by  using  strings  of  different  lengths. 
— The  pitch  of  any  sound  depends  upon  the  rapidity  of 
vibrations  ;  but  according  to  the  first  law  of  vibrating 
strings,  the  rapidity  of  vibration  is  greater  as  the  string 
is  made  shorter.     To  obtain  sounds  of  different  pitch, 
we  may  then  use  strings  of  different  lengths. 

Now,  suppose  we  would  know  the  lengths  of  eight 
strings  of  the  same  weight  and  tension,  which  would 
give  the  eight  notes  of  the  scale.  We  have  learned 
that  the  number  of  vibrations  per  second  is  inversely  as 
the  length  of  the  cord,  and  we  have  learned  also  that 
the  relative  number  of  vibrations  for  the  eight  notes  are 


176  NATURAL    PHILOSOPHY. 

expressed  by  the  series  1,  f,  £ ,  f,  f-,  f,  V,  2.  Then 
mwrtf  the  terms  of  this  series,  and  they  must  express  the 
relative  lengths  of  cord  to  produce  the  notes.  They  will 
be  1,  -I,  £,  f,  f,  f,  A,  f  Knowing  ^  the  length  of  the 
string  to  give  the  fundamental,  it  is  easy  to  calculate 
the  lengths  of  all  the  others.  Let  us  start  with  a  string 
18  inches  long  for  the  first  note ;  the  second  must  be 
|  x  18  ;  the  third  must  be  |-x  18 ;  the  fourth,  must  be 
jf  x  18,  and  so  on  until  the  eighth,  which  must  be  %  x  18. 

3.  Pitch  is  varied  l>y  using  strings  of  different  ten* 
sion. — According  to  the  second  law  of  vibrating  strings 
[see  (46.)],  the  number  of  vibrations  made  in  a  second 
increases  when  the  tension  increases.     Hence  the  pitch 
of  sound  made  by  the  string  will  be  higher  when  the 
tension  is  made  greater. 

4.  Pitch    is   varied  ty  using  strings    of  different 
weights. — According  to    the  third    law  of   vibrating 
strings,  the  number  made  in  one  second  varies  inversely 
a*  the  square  root  of  the  weight  of  the  strings.     Hence 
tiie  pitch  of  the  sound  will  be  higher,  when  the  string 
which  makes  it  is  lighter. 

H. — WIND    INSTRUMENTS. 

B. — The  organ  and  the  clarionet  are  examples  of 
wind  instruments.  In  the  organ,  sounds  are  made  by 
vibrating  columns  of  air  in  pipes,  sometimes  aided  by 
the  vibrations  of  a  slender  and  elastic  tongue,  called 
a  reed.  (See  Tyndall  on  Sound.)  In  the  clarionet  the 
sounds  are  always  made  by  air  vibrations  aided  by  a  reed. 

The  pitch  of  sounds  in  pipes,  depends  upon  the 
lengths  of  the  pipes.  A  pipe  to  produce  the  lowest 
note  in  music,  must  be  32  ft.  in  length,  and  the  pitch  of 


NATURAL    PHILOSOPHY.  177 

tones  from  other  pipes  will  vary  inversely  as  the  length 
of  the  pipes. 

Organ  pipes  are  sometimes  open  at  the  top,  and 
sometimes  closed.  An  open  organ  pipe  yields  a  note 
an  octave  higher  than  a  closed  pipe  of  the  same  length. 
A  closed  pipe,  to  give  the  lowest  note  in  music,  Deed 
only  be  16  ft.  in  length. 


178  NATURAL    PHILOSOPHY. 


CHAPTEK    VI. 


MODES  OF  VIBRATION.— IL  SOUND. 

§  1.    ON   THE   NATURE    OF    LIGHT,   AND  THE   LAWS   O*     HI 
TRANSMISSION. 

(59.)  HEAD  (51).  Light  is  thought  to  be  the  effect  of 
vibrations  in  an  ether  which  fills  all  space  not  filled  by 
other  matter.  These  vibrations  are  produced  by  lumin- 
ous bodies,  and,  when  transmitted  to  the  eye,  cause 
vision. 

1.  Light  is  the  effect  of  vibrations. — It  was   once 
thought   that  light    consists   of   minute  particles  of 
matter  thrown  in  great  abundance  from  the  sun  and 
some  other  bodies :  it  is  now  generally  believed  that 
light    is    a    kind    of  vibration.      But  light  will  pass 
through  the  most  perfect  vacuum  that  can  be  made : 
what  can  be  left  to  vibrate?    Moreover,  the  atmosphere 
extends  but  a  few  miles  above  the  earth,  yet  the  light 
from  the  sun  comes  in  floods  through  the  vast  distance 
which  separates  these  bodies:  what  can  there  be  be- 
tween the  sun  and  the  earth,  whose  vibrations  bring  to 
as  the  sunlight  ? 

2.  The  ether. — Philosophers  assume  that  there  is  a 
thin,  elastic  substance  called  ether,  much  finer  and  rarer 
than  air,  which  fills  all  the  spaces  between  the  heavenly 


NATURAL     PHILOSOPHY.  179 

bodies,  and  enters  into  all  the  spaces  between  molecules 
jf  matter  in  every  form.  The  vibrations  of  this  ether 
carry  light  wherever  it  goes,  through  a  vacuum,  through 
celestial  spaces,  through  bodies  like  glass,  and  through 
the  substances  of  the  eye,  until  it  strikes  the  nerves  of 
eight. 

"When  a  gas  jet  is  suddenly  lighted  in  a  dark  room, 
every  eye  present  is  dazzled  by  the  brightness  of  ihe 
light.  The  explanation  is  this.  The  heated  gaa  makes 
the  ether  vibrate.  This  ether  is  between  the  particles 
of  the  air,  and  between  the  particles  of  the  eye.  Its 
vibrations,  starting  from  the  gas  jet,  go  through  the 
air  and  into  the  eye,  and  when  they  reach  the  delicate 
nerves  in  the  back  part  of  this  organ  we  are  made  con- 
scious of  the  presence  of  light 

3.  Luminous  ladles.—  Bodies  which  shine  by  their 
own  light  are  called  luminous  bodies.  They  are  bodiea 
which  can  make  the  ether  vibrate.  Bodies  which 
shine  only  by  light  which  they  receive  from  others  are 
called  non-luminous  bodies.  They  can  not  make  the 
ether  vibrate.  The  sun  is  a  luminous  body:  so  is  a  red- 
hot  iron  ball.  All  flames  are  luminous  bodies.  The 
moon  is  non-luminous.  Almost  all  bodies  on  the  earth 
are  non-luminous :  the  light  which  they  give  to  us  is 
light  which  the  sun  first  gave  to  them. 

(60.)  Kays  of  light  are  transmitted  through  some 
media  more  freely  than  through  others  but  always 
according  to  two  laws  : — 

1st.  In  a  medium  of  uniform  density,  light  goes  in 
straight  lines  with  a  uniform  velocity. 

2d.  The  intensity  of  light  varies  inversely  as  the 
iquare  of  the  distance  from  its  source. 


180  NATURAL    PHILOSOPHY. 

The   art  of  Photometry  depends  upon  this  second 
law. 


1.  Rays  of  light. — A  single  line  of  light,  or  more 
accurately  the  path  of  a  single  vibration,  is  called  a 
ray  of  light.     But  the  smallest  portion  of  light  which 
can  be  separated  by  experiment,  consists  of  many  rays. 
A  ray  of  light  is  quite  too  delicate  a  thing  to  be  seen. 
A  collection  of  parallel  rays  is  called  a  beam  of  light. 
A  collection  of  rays  which  diverge  from  a  point,  or 
•which  converge  toward  a  point,  is  called  a  pencil  of 
light. 

2.  Rays  of  light  are  transmitted. — Some  substances 
permit  light  to   pass  through  them  freely;  they  are 
said  to  be  transparent.     Air  and  water  are  examples 
of  transparent  bodies.     Others,  such  as  iron  and  wood, 
appear  to  forbid  the  passage  of  light  through  them : 
they  are  said  to  be  opaque.     But   no  substance  will 
*  .ansmit  all  the  light  which  it  receives ;  even  the  air  is 
not  perfectly  transparent.     On  the  other  hand,  no  sub- 
stance will  stop  all  the  light  which  falls  upon  it ;  even 
gold,  when  a  very  thin  leaf  of  it  is  examined,  can  be 
seen  to  transmit  light.     All  substances  are  doubtless 
able  to  transmit  light  in  some  degree. 

3.  Light  moves  in  straight  lines. — That  light  moves 
in  straight  lines  is  shown  by  numerous  familiar  facts. 
We  can  not  see  through  a  crooked  tube,  simply  because 
light  can  not  purs  le  a  crooked  path.     And  again  :  who 
has  not  seen  the  sunlight  coming  through  the  shutters 
of  a  half-dark rvned  parlor,  spotting  the  opposite  wall 
with  circles  of  light  ?    The  sun,  the  hole  in  the  shutter, 
and  the  spot  on  the  wall,  are  always  in  the  same  straight 
line.     Let  the  air  of  the  room  be  sprinkled  with  dust, 


NATURAL    PHILOSOPHY.  18] 

and  the  paths  of  the  sunbeams  are  seen  streaking  the 
air  with  bars  of  light. 

4.  With  uniform  velocity.  —  Light  travels  through 
space  with  a  uniform  velocity  of  about  192,000  miles  a 
second.      This  number  has  been  found  by  observing 
the   eclipses  of  one  of  the   moons  of  Jupiter.     The 
time  when  the  eclipse  should  begin  can  be  calculated 
by  an  astronomer  with  great  accuracy.     But  it  is  found 
that  when  the  earth  is  in  that  part  of  its  orbit  nearest 
to  Jupiter,  the  eclipse  begins  16  minutes  and  36  seconds 
sooner  than  it  appears  to  when  the  earth  is  in  the  op- 
posite part  of  its  orbit.     It  must,  therefore,  take  light 
16  minutes  and  36  seconds  to  go  across  the  earth's  orbit 
"When  this  distance  is  known  and  divided  by  the  number 
of  seconds  the  velocity  of  light  is  found.    Calling  the  dis- 
tance from  the  earth  to  the  sun,  ninety-five  millions  of 
miles,  the  result  is  about  192,000  miles  a  second.*   For 
all  distances  on  the  surface  of  the  earth,  the  passage  of 
light  may  be  considered  instantaneous.     It  would  go 
quite  around  the  world  almost  seven  times  in  a  single 
second. 

5.  The  second  law. — That  the  intensity  of  light  is 
less  as  we  go  farther  from  the  luminous  body,  is  a  fact 
familiar  to  all:  the  rate  at  which  it  diminishes  is  not  so 
apparent.     That  the  intensity  varies  inversely  as  the 
square  of  the  distance  may  be  easily  proved  by  experi- 
ment. 

A  square  piece  of  stiff  card- board  A  (Fig.  78),  is  placed 
in  front  of  another  (B)  very  much  larger.  If  now,  a 
candle-flame  be  placed  in  front  of  the  small  card,  a 
shadow  will  be  cast  upon  the  large  one.  This  shadow 

*  For  Foucault'a  method  of  finding  the  velocity  of  light,  see  Siil*- 
man's  Phys.  p.  294. 


182 


NATURAL     PHILOSOPHY. 


will  be  larger,  as  the  sm."  ll  card  is  moved  nearer  to  the 
flame,  it  will  be  smaller  as  it  is  moved  the  other  way. 
Fig.  78.  The   figure  is  in- 

tended to  show 
the  small  card  to 
be  just  J  as  far 
from  the  flame  aa 
the  large  one.  In 
this  case  the  shad- 
ow will  be  found 
to  be  exactly  16 
times  as  large  as  the  card  in  front  of  it.  Now,  the  same 
amount  of  light  which  is  spread  over  the  small  card 
would,  if  it  could  go  on,  just  cover  the  place  of  this 
shadow.  But  if  the  same  amount  of  light  is  spread 
over  16  times  as  much  surface  in  one  case  as  in  another, 
it  can  be  only  T^  as  intense.  At  4  times  the  distance 
from  the  luminous  body,  in  this  case,  the  intensity  of 
the  light  is  ^  as  great.  At  3  times  the  distance,  the 
light  would,  in  the  same  way,  be  found  to  be  -£  as  in- 
tense. In  other  words ;  the  intensity  of  light  varies 
inversely  as  the  square  of  the  distance  from  the  lumin- 
ous body. 

6.  Photometry. — It  is  often  desirable  to  compare  the 
illuminating  powers  of  different  flames.  The  art  of 
doing  this  is  called  photometry .  The  simplest  method 
is  to  place  the  two  flames  at  such  distances  from  a  screen, 
that  the  intensities  of  the  light  they  shed  upon  it  shall  be 
equal ;  the  illuminating  powers  of  the  flames  must  then 
be  as  the  squares  of  these  distances.  Suppose,  for  ex- 
ample, that  we  wish  to  know  how  many  times  more 
xight  one  candle  will  give  than  another  of  inferior 
quality.  Let  a  slender  rod  B  (Fig.  T9),  be  put  just  in 


NATURAL    PHILOSOPHY. 


183 


front  of  a  white  screen  A,  and  then  move  the  flames  to 
such  distances,  that  the  two  shadows  of  the  rod,  falling 

Fig.  79. 


side  by  side  upon  the  screen,  shall  appear  to  be  of  equal 
darkness.  The  intensities  of  their  lights  on  the  screen 
must  then  be  equal.  Measure  the  distances  from  the 
flames  to  the  screen :  the  amounts  of  light  they  give 
will  be  as  the  squares  of  their  distances.  One  being 
twice  as  far  away  as  the  other,  it  gives  four  times  as 
much  light. 

§    2.    ON    THE    REFLECTION    OF   LIGHT. 

(61.)  When  light  in  passing  through  one  medium 
comes  against  the  surface  of  another,  only  a  part  will  be 
transmitted,  another  part  will  be  reflected,  obeying  the 
following  law : — 

The  angles  of  incidence  and  reflection  must  be  equal, 
and  in  the  same  plane. 

1.  Reflection. — The  reflection  of 
light  is  in  all  respects  like  the  reflection 
of  sound  [see  (55.)  1].  The  same  terms 
are  used  to  describe  it ;  the  same  figure 
may  be  reproduced  to  illustrate  it 
Thus  in  Fig.  80,  the  line  I  A,  may  re- 
present a  beam  of  light  passing  through 
air  and  striking  upon  the  surface  of 
a  plate  of  glass  at  A.  One  part  of  the 


Fig.  80. 


NATURAL    PHILOSOPHY. 

beam  will  enter  the  glass  and  emerge  again  on  the  other 
side,  but  another  part  will  be  thrown  back  into  the  aii 
in  the  direction  A  R.  The  beam  I  A  is  the  incident 
beam.  The  beam  A  R  is  the  reflected  beam.  The 
point  A  is  the  point  of  incidence. 

2.  The  law  of  reflection. — The  reflection  of  light  ia 
also  governed  by  the  same  law  as  the  reflection  of  sound. 
The  angle  I  A  P  (Fig.  80),  is  the  angle  of  incidence. 
The  angle  P  A  R  is  the  angle  of  reflection.  Those 
two  angles  must  be  equal. 

How  various  and  beautiful  are  the  phenomena  which 
this  principle  of  reflection  explains  I  The  sky,  with  all 
its  floating  clouds  or  shining  stars,  is  painted  in  every 
pool  of  water,  because  the  light  from  them,  falling  on 
the  surface  of  the  water,  is  reflected  to  our  eyes. 
Rocks,  and  shrubbery,  and  dwellings  along  the  shore, 
are  pictured  in  the  quiet  waters  of  the  lake,  with  skill 
exceeding  that  of  any  human  artist. 

Vision  is  produced  by' reflected  light.  How  seldom 
do  we  receive  the  direct  rays  of  the  sun  into  the  eye ; 
how  rarely  indeed,  do  we  look  directly  upon  any  lu- 
minous body !  But  in  all  other  cases  we  see  objects 
only  by  reflected  light.  The  sunbeams  fall  upon  all 
objects  exposed  to  them,  and,  bounding  from  their  sur- 
faces, enter  the  eye,  and  we  see  them  in  the  direction 
from  which  the  reflected  rays  have  come. 

(62.)  The  effects  of  mirrors  are  explained  by  reference 
to  the  law  of  reflection. 

Rays  of  light  reflected  by  a  plane  mirror  have  the 
same  relation  to  each  other  as  before  reflection ; 

But  the  effect  of  a  concave  mirror  is  to  collect  the 
rays -of  light  which  are  reflected  by  it; 


NATURAL    PHILOSOPHY.  135 

While  a  convex  mirror   always  separates   the  rays 
which  it  reflects. 

1.  Mirrors.— Any  surface  smoothly  polished  that  will 
reflect  nearly  all  the  light  which  falls  upon  it,  is  called 
a  mirror.     The  smooth  surface  of  quiet  water  is  a  very 
perfect  mirror.     Artificial  mirrors  are  generally  made 
of  metal  or  of  glass.     If  made  of  glass,  a  thin  film  of 
mercury  is  spread  over  one  side,  and  the  smooth  surface 
of  this  metallic  coating  is  really  the  reflecting  surface. 
Mirrors  are  either  plane  or  curved.     Of  the   curved 
mirrors  there  are  two  varieties,  the  concave  and  the 
convex  mirrors. 

2.  The  effect  of  plane  mirrors. — The  rays  of  light 
which  fall  upon  a  mirror  may  be  parallel,  or  converg- 
ing, or  diverging,  but  can  have  no  other  relation.     Now, 
let  the   mirror  be  repre-  Fig  81 

sen  ted  by  the  straight  line 
A  B  (Fig.  81),  and  sup- 
pose, first,  that  it  receive 
two  parallel  rays  repre- 
sented by  the  lines  a  c 
and  5  d.  At  the  point  of  incidence  c,  erect  a  per- 
pendicular to  the  surface  A  B.  The  angle,  a  c  g, 
will  be  the  angle  of  incidence.  Then  draw  the  line 
c  f,  so  as  to  make  the  angle  of  reflection,  g  c  f, 
equal  to  the  angle  of  incidence,  and  c  f  must  be  the 
direction  of  the  ray  reflected  from  the  point  c.  Again  : 
at  the  point  of  incidence  d,  erect  a  perpendicular  and 
draw  the  line  d  e,  making  the  angle  of  reflection  equal 
to  the  angle  of  incidence,  and  this  line  must  represent 
the  ray  reflected  from  the  point  d.  It  will  be  found 
that  the  reflected  rays,  c  f  and  d  e,  will  be  par- 
allel 


186 


NATURAL    PHILOSOPHY. 


Fig.  88. 


Suppose,  second :  that  two 
rays,  a  c  and  b  d  (Fig.  82), 
are  converging  and  strike 
the  mirror  at  the  points  <j 
and  d.     By    making   the 
angles   of    incidence    and 
reflection  equal,  exactly  as 
t  was  done  in  the  preceding  case,  we  find  that  the  re- 
flected rays  will  take  the  directions  c  e  and  d  e,  converg- 
ing to  the  point  e. 

Suppose,  third :  that 
the  rays  are  diverging. 
Represent  them  by  lines 
a  c  and  ad  (Fig.  83).  Erect 
the  perpendiculars  and 
construct  the  angles  of 
incidence  and  reflection 
equal,  and  the  directions 
of  the  reflected  rays  will 
be  c  e  and  df,  diverging  from  each  other. 

In  each  of  these  three  cases,  the  reflected  rays  have 
the  same  relation  as  the  incident  rays. 

3.  The  effect  of  concave  'mirrors. — We  will  notice 
only  those  concave  mirrors  whose  surfaces  are  spherical. 
If  we  know  the  direction  of  the  incident  rays,  we  can 
find  the  direction  of  the  reflected  rays  by  making  the 
angle  of  reflection  equal  to  the  angle  of  incidence.  To 
construct  the  angle  of  incidence,  we  must,  as  in  the 
Diane  mirror,  erect  a  perpendicular  to  the  concave 
ourfaco  at  the  point  of  incidence,  and  all  difficul- 
ty disappears  when  we  remember  that  a  perpen- 
dicular to  any  spherical  surface  is  the  radius  of  th* 


NATURAL     PHILOSOPHY. 


187 


In  Fig.  84,  M  N  rep-  Fig.  M. 

resents  a  section  of  a 
concave  mirror.  The 
point  C  represents  the| 
center  of  curvature, 
that  is,  the  center  of 
the  hollow  sphere,  of 
whose  concave  surface 
the  mirror  is  a  part. 
Now,  if  E  A  and  D 
B  represent  two  par- 
alld  incident  rays,  and 
we  would  find  the  direction  they  take  after  reflection, 
we  may  draw  the  radii,  C  A  and  C  B,  making  the 
angles  of  incidence,  E  A  C  and  D  B  C,  and  then  draw  the 
lines  A  F  and  B  F,  so  as  to  make  the  angles  of  reflection 
equal  to  these.  By  so  doing,  we  find  that  the  reflected 
rays  converge  and  cross  each  other  at  the  point  F. 

In  Fig.  85,  the 
lines,  E  A  and  D 
B,  represent  con- 
vergingrays.  By 
constructing  the 
angles  of  inci- 
dence and  reflec- 
tion in  the  same 
way  as  before,  we 
find  that  the  re- 
flected rays  cross 
each  other  at  the 
point  F,  converging  faster  after  reflection  than  before. 

In  the  same  figure,  F  A  and  F  B  may  represent  di- 
verging rays,  striking  the  mirror  at  the  points  A  and 


Fig.  85. 


188 


NATURAL    PHILOSOPHY. 


Fig.   86, 


B.  By  constructing  the  angles  of  incidence  and  reflcc 
tion  equal,  we  find  the  reflected  rays  taking  the  direc- 
tions A  E  and  B  D,  diverging  less  after  reflection  than 
before. 

Now,  since  parallel  rays  are  made  converging,  and 
converging  rays  are  made  more  converging,  while  di- 
verging rays  are  made  to  diverge  less,  we  may  say  that 
the  general  effect  of  a  concave  mirror  is  to  collect  rays 
of  light. 

A  focus  is  any  point  where  rays  of  light  cross,  or  ap- 
pear to  cross,  after  reflection.  The  points  F,  in  Figs. 
84  if.ul  85,  are  foci.  The  axis  of  a  mirror  is  a  straight 
line  drawn  through  the  center  of  curvature  and  the 
middle  point  of  the  mirror. 

In  Fig.  86,  the 
line  C  A  is  the 
axis  of  the  mirror 
M  N,  whose  center 
of  curvature  is  at 
C.  The  focus  of 
rays  that  are  par- 
allel to  the  axis, 
and  fall  upon  the 
mirror  near  its 
middle  point,  is 
called  the  princi- 
pal focus.  If  the  rays  B  E  and  D  H  (Fig.  86),  are  near 
to,  and  parallel  to  the  axis  C  A,  they  will,  after  reflec- 
tion, cross  each  other  at  the  point  F,  and  this  point  is 
the  principal  focus  of  the  mirror.  The  principal  focus 
is  on  the  axis,  half  way  between  the  center  of  curvature 
and  the  mirror. 

4.  The  effect  of  convex  mirrors. — In  Fig.  8  7,  a  convex 


NATURAL    PHILOSOPHY.  189 

mirror  is  represented  by  M  N,  its  center  of  curvature 
by  the  point  C.  Two  parallel  rays  of  light,  E  A  and 
D  B,  strike  the  mirror  at  the  points  A  and  B.  To 


Fig.  87. 


construct  the  angles  of  incidence,  we  must  erect  per- 
pendiculars to  the  surface  at  these  points.  The  per- 
pendiculars are  the  radii,  C  A  and  C  B,  extended  beyond 
the  convex  surface  of  the  mirror.  By  making  the 
angles  of  reflection  equal  to  the  angles  of  incidence, 
the  reflected  rays  are  found  to  take  the  directions  A  P 
and  B  H.  We  notice  that  parallel  rays  are  rendered 
diverging. 

So  we  might  show  that  diverging  rays  would  be  made 
more  diverging,  and  that  converging  rays  would  t>e 
made  to  converge  less.  We  say,  therefore,  that  the  gen- 
eral effect  of  a  convex  mirror  is  to  separate  rays  of  light. 

(63.)  When  the  light  reflected  from  a  mirror  enters 
the  eye,  we  see  an  image  of  the  object  from  which  the 
light  proceeds. 


190 


NATURAL    PHILOSOPHY. 


The  image  of  any  point  will  always  be  found  where 
the  rays  of  light  which  go  from  that  point,  either  meet, 
or  appear  to  meet,  after  reflection. 

1.  Images    by   reflection.  —  When  a  person  stanos 
before  a  looking-glass^  numberless  rays  ot  light  from 
every  point  of  his  countenance  fall  upon  it.     These 
rays  are  reflected,  and  many  of  them  are  thrown  into 
the  eye.      Those  which  enter  the  eye,  cause  him  to 
see  his  image  in  the  glass. 

2.  The  image   of  a  point. — Now,  if  the   rays   of 
light,  which  form  the  image  in  the  glass,  were  visible, 
the  person  would  be  able  to  trace  them  back  from  the 
eye,  converging  toward  the  points  on  the  glass  from 
which  they  are  reflected,  and  they  would   appear  as 
if -they  came    from   points   in  the  image  behind   the 
glass. 

pig.  sa  This  will  be  understood 

by  means  of  Fig.  88.  Let 
M  N  represent  a  plane 
mirror.  From  the  point 
A,  numberless  rays  fall 
upon  the  mirror,  some 
of  which,  after  reflection, 
will  enter  the  eye,  sup- 
posed to  be  at  O.  Two 
of  these  rays  are  rep- 
resented in  the  figure. 
The  eye  will  receive  these 
rays  as  if  they  came  from 

the  point  0,  and  this  point  a  is  the  image  of  the  point 

A,  from  which  the  rays  proceed. 

(64.)  The  image  formed  by  a  plane  mirror  is  always 


NATURAL    PHILOSOPHY. 


191 


as  far  behind  the  mirror  as  the  object  is  in  front  of  it ; 
the  same  size  as  the  object,  and  erect. 

1.  Images  by  plane  mirrors. — We  are  now  prepared 
to  see  how  looking-glasses  make  such  perfect  images  of 
all  objects  placed  in  front  of  them.  Suppose  an  arrow 
A  B,  placed  before  a  mirror  (Fig.  89).  Let  us  con- 
struct its  image.  From  the 
vast  number  of  rajs  which 
go  from  A  to  the  glass,  select 
two  which  fall  upon  it  very 
near  together,  at/"  and  g.  By 
making  the  angles  of  reflec- 
tion equal  to  the  angles  of  in- 
cidence, we  find  the  reflected 
rays  taking  the  directions  f 
P,  and  g  O.  Now,  if  the  ej  e 
be  placed  at  E,  it  will  receive 
these  reflected  rays  as  if  they 
came  from  the  point  a.  Again, 
select  two  rays,  which,  going  from  the  otner  end  of  the 
arrow  B,  strike  the  mirror  at  points  near  together  at 
c  and  d,  so  that  after  reflection  they  cnn  enter  the 
same  eye  at  E.  These  rays  will  appear  to  have  come 
from  b.  From  all  points  between  A  and  B,  rays  of 
light  will  go  to  the  mirror ;  and,  being  reflected,  will 
enter  the  eye  at  E,  and  appear  to  have  come  from 
points  between  a  and  b.  The  image  of  the  arrow, 
A  B,  will  thus  be  seen  at  a  b.  We  may  describe  this 
image  thus :  the  image  made  by  a  plane  mirror  u 
'always  behind  the  mirror,  just  as  far  as  the  object  is  in 
front  of  it,  of  the  same  size  as  the  object,  and  erect. 


(05.)  If  an  object  be  placed  in  front  of  a  concave 


192  NATURAL     PHILOSOPHY. 

mirror,  an  inverted  image  may  be  formed  on  the  same 
side  of  the  mirror.  To  explain  this  remember  thaf, 
the  image  of  any  point  will  be,  where  rays  of  light  eithei 
meet,  or  appear  to  meet,  after  reflection. 

1.  Images  are  formed. — The  brilliant  inner  surface 
of  a  silver  spoon  shows  the  image  of  a  person  who 
looks  upon  it,  but  it  will  be  curiously  different  from 
his  image  seen  in  a  looking-glass.     It  is  very  small ;  it 
is  inverted;  and,  moreover,  by  careful  attention,  the 
person  sees  his  picture  standing  in  the  air  between  him- 
self and  the  surface  of  the  spoon.     Nor  is  this  all  ;  the 
picture  in  the  air  will  grow  larger  or  smaller,  or  it  may 
disappear  altogether,  as  the  spoon  is  moved  toward  or 
from  the  face  of  the  observer. 

If  a  spherical  concave  mirror  of  small  curvature  be 
at  hand,  a  beautiful  experiment  will  illustrate  its  power 
to  form  images.  Let  a  beam  of  sunlight  pass  through 
an  opening  in  the  shutter  of  a  dark  room.  In  the  path 
of  this  beam,  at  a  convenient  distance  from  the  win- 
dow, place  a  picture  of  a  butterfly  or  other  object, 
painted  in  transparent  colors  upon  glass.  The  concave 
mirror  placed  in  front  of  the  picture,  so  as  to  receive 
the  light  which  has  come  through  it,  will  reflect  the 
rays  upon  the  wall  above  the  window,  and  if  its  dis- 
tance from  the  picture  is  just  right,  a  magnificent  image 
of  the  butterfly,  much  larger  than  the  picture,  and  with 
its  head  downward,  will  be  seen  upon  the  wall. 

2.  The  images   of  points. — How   is   this   beautiful 
effect  produced?     Can  we  find  the  images  of  points 
[see  (63.)  2]  of  the  object  by  tracing  the  reflected  rays 
which  produce  them  ?     Let  M  ]Sr  (Fig.  90),  represent,  a 
section  of  a  concave  mirror,  and  suppose  an  arrow,  A  B, 
in  front  of  it.     Select  two  rays  of  light  which,  going 


WAT  URAL     PHILOSOPHY.  193 

from  the  point  A,  fall  upon  the  mirror  at  the  points 
D  and  E.     After  reflection  they  will  cross  each  other 


Fig.  90. 


at  A'.  Again  select  two  rajs,  which,  going  from  the 
point  B,  fall  upon  the  mirror  at  the  points  II  and  F. 
After  reflection  they  will  cross  each  other  at  B'. 
Other  points  in  the  object  will  send  rays  to  the  mirror, 
which,  after  reflection,  will  cross  each  other  at  points 
between  A'  and  B'.  In  this  way  a  large  and  inverted 
image  is  made  in  the  air  at  A'  B'. 

(66.)  The  position  and  size  of  the  image  ^will  depend 
npon  the  distance  of  the  object  from  the  mirror.  We 
will  notice  three  well-marked  cases  : — 

1st.  When  the  object  is  beyond  the  center  of  curv- 
ature. 

2d.  When  the  object  is  between  the  center  of  curva- 
ture and  the  principal  focus. 

3d,  When  the  object  is  between  the  principal  focng 
and  the  mirror. 

1.  The  object  beyond  the  center. — We  are  now  pre- 
pared to  see  how  the  mirror  forms  its  images  in  the  air. 
Let  M  N  (Fig.  91)  represent  a  section  of  a  concave 

9 


194  NATURAL     PHILOSOPHY. 

mirror,  whose   center  of  curvature  is  C,  and    whose 
principal  focus  is  F.      Suppose  an  arrow  A  B,  to  be 

Fig.  91. 


put  in  front  of  the  mirror,  beyond  the  center  of  curva 
ture.  The  rays  of  light  from  the  top  of  the  arrow  A, 
will,  after  reflection  from  the  mirror,  cross  each  other 
at  the  point  A'.  Those  which  go  from  the  bottom  of 
the  arrow  B,  will,  after  reflection,  cross  each  other  at 
B'.  From  points  of  the  arrow  between  A  and  B,  the 
light  which  falls  upon  the  mirror,  will  be  collected  into 
corresponding  points  between  A'  and  B'.  A  perfect 
image  of  the  arrow  will  thus  be  formed  at  A7  B'.  In  this 
case  we  observe  that  the  image  is  between  the  center  of 
curvature  and  the  principal  focus,  inverted,  and  smaller 
than  the  object. 

This  case  was  illustrated  by  the  experiment  with 
the  silver  spoon. 

2.  The  object  between  the  center  and  focus. — Now,  let 
us  suppose  that  in  this  same  Fig.  91  an  arrow  B'  A', 
with  its  head  pointing  downward,  is  placed  between  the 
center  of  curvature  and  the  principal  focus.  The  rays 
of  light  from  the  point  B',  striking  the  mirror  at  a  and  b 
will,  after  reflection,  cross  each  other  at  the  point  B, 
those  from  A',  alter  reflection,  will  cross  each  other 
at  A,  and  the  image  of  the  arrow  will  be  formed 
at  A  B.  In  this  case,  we  observe  that  the  image  will 


NATURAL     PHILOSOPHY.  39? 

be   leyond  the  center  of  curvature,  inverted,  ai\d  en- 
larged. 

This  case  was  illustrated  by  the  experiment  with  the 
picture  of  the  butterfly. 

3.  The  object  'between  the  focus  and  the  mirror.-  — 
When  the  object  is  gradually  moved  from  the  center 
toward  the  focus,  the  image  will  rapidly  move  farther 
and  farther  away,  until,  when  the  object  has  reached 
the  focus,  the  image  will  be  at  an  infinite  distance  in 
front  of  the  mirror,  and  of  course,  invisible.  But  let 
the  object  be  carried  a  little  farther,  so  as  to  be  between 
the  focus  and  the  mirror,  and  the  ima<?e  suddenly  leaps 
from  its  distant  place  in  front  of  the  mirror,  to  a  position 
behind  it. 

To  illustrate  the  formation  of  this  image  behind  the 
mirror,  let  A  B  (Fig.  92),  represent  an  object  between 
the  focus  F,  and  the  mir-  Fig.  92. 

ror  M  M'.  Two  rays  of 
light  from  the  top  of  the 
object  strike  the  mirror  at 
H,  and  are  reflected  to  the 
point  E.  To  an  eye  placed 
there,  these  rays  would 
appear  to  have  come  from 
the  point  a  behind  the 
mirror.  Two  rays  from 
the  bottom  of  the  object  falling  upon  the  mirror  at  K, 
will  be  reflected  so  as  to  enter  the  same  eye  at  E,  and 
will  seem  to  have  come  from  the  point  b.  Joining  the 
points  a  and  £,  we  have  the  entire  image  constructed.  In 
tnis  case  we  observe  that  the  image  is  behind  the  mir- 
*w,  erect,  and  larger  than  the  olject. 

(67.)     The   images   formed   by  convex   mirrors  are 


196  NATURAL    PHILOSOPHY. 

always  behind  the  mirror,  erect,  and  smaller  than  the 
object. 

1.  Images  by  convex  mirrors.  —  The  bottom  of  a  silver 
spoon  will  serve,  in  a  homely  way,  to  illustrate  the  effects 
of  a  convex  mirror.  A  person  looking  upon  it  will  see 
his  own  image,  apparently  in  the  metal  of  the  spoon, 
erect,  but  very  small.  The  following  diagram  will  il- 
lustrate the  formation  of  these  images. 

j^  w  The  object  D  E,  is  placed  in  front 

of  the  convex  mirror  A  B,  whose 
center  of  curvature  is  at  C.  Two 
rays  of  light  from  D,  may  be  traced 
after  reflection  to  the  points  H  and 
K,  and  if  an  eye  can  receive  these 
rays,  they  will  seem  to  come  from 
the  point  d.  In  like  manner,  rays 
from  the  point  E,  after  reflection 
from  the  mirror,  may  enter  the 
same  eye,  and  appear  to  have  come 
from  e.  The  image  of  the  object  will  thus  be  found  at 
d  6)  behind  the  mirror,  erect,  and  smaller  than 


/  _  §  3.    ON    THE    REFRACTION    OF    LIGHT. 

(68.)  When  light  passes  from  one  medium  into  an- 
other of  different  density,  it  is  refracted,  obeying  the 
following  laws  :  — 

1st.  In  passing  into  a  denser  medium,  light  is  bent  to- 
ward a  perpendicular  to  the  surface  at  the  point  of 
incidence. 

2d.  In  passing  into  a  rarer  medium,  light  is  bent  from 
the  perpendicular. 

1.  Refraction.-  -The  refraction  of  light  is  similar  to 


NATURAL     PHILOSOPHY. 


197 


the  refraction  of  sound  [see  (54.)  2].     The  same  terms 
are  used  to  describe  it,  and  the  Figj  94t 

same  figure  might  be  made  to 
illustrate  it.  A  simple  experi- 
ment will  suit  our  purpose  bet- 
ter. Through  a  small  opening 
in  the  shutter  of  a  darkened 
room,  let  a  beam  of  sunlight 
enter,  and  fall  obliquely  upon 
the  surface  of  water  held  in  a 
glass  vessel  (a  b  c  d,  Fig.  94). 
If  the  water  has  been  made  tur- 
bid by  the  addition  of  a  little  soap,  and  the  air  above 
it  misty,  by  sprinkling  into  it  the  dust  of  a  chalk-brush, 
the  beam  of  light  will  be  distinctly  seen  in  both,  abso- 
lutely straight,  except  at  the  surface  of  the  water,  where 
it  will  be  very  considerably  bent.  Its  path  is  repre- 
sented by  the  broken  line  A  B  D. 

2.  The  firxt  law  of  refraction. — If  now,  a  perpen- 
dicular F  E,  be  erected  to  the  refracting  surface  at  the 
point  of  incidence  B,  we  see  that  the  rays  A  B,  instead 
of  moving  in  a  straight  line,  onward  to  C,  will  be  bent 
toward  the  perpendicular.     Water  is  denser  than  air. 
In  going  from  the  rarer  to  the  denser  medium,  the  light 
is  bent  toward  the  perpendicular. 

3.  The  second  law  of  refraction. — Let  us  suppose  that 
D  B  represents  a  beam  of  light  going  from  the  water 
into  the  air  at  B ;  it  will  take  the  direction  B  A,  in- 
stead of  going  on  in  a  straight  line  toward  P,  being 
bent  from  the  perpendicular  F  E.     In  passing  from  tho 
denser  medium  into  the  rarer,  the  light  is  bent  from 
the  perpendicular. 

Many  phenomena  in  nature  may  be  explained  by 


198  NATURAL    PHILOSOPHY. 

reference  to  these  principles.  When,  for  example,  au 
oar  is  dipped  into  clear  and  quiet  water,  it  appearg 
broken  at  the  surface.  The  light  comes  to  the  eye  from 
all  points  of  the  oar.  From  that  part  which  is  above 
ivater  it  comes  in  straight  lines  through  the  air,  but 
from  the  part  under  the  water  the  light  coming  up  into 
the  air,  is  bent  at  the  surface.  The  eye  which  receives 
these  bent  rays  traces  them  back  in  straight  lines,  and 
the  oar,  from  which  they  come,  is  thus  made  to  appear 
to  be  where  it  really  is  not. 

(69.)  Some  substances  refract  light  more  than  others. 
Their  relative  refracting  powers  are  indicated  by  cer- 
tain numbers,  which  are  called  indices  of  refraction. 

1.  The  index  of  refraction. — We  may  best  explain 
the  meaning  of  this  term  by  means  of  the  following  dia- 
grain.  Suppose  a  small  beam  of 
[light  L  A  (Fig.  95).  to  be  passing 
from  air  into  water.  It  will  be  bent 
at  A,  and  go  on  in  the  direction  of 
A  K.  Now,  with  the  point  A  as  a 
[center,  and  with  any  convenient  ra- 
Idius  describe  a  circumference.  Let  a 
perpendicular  B  C,  be  erected  to 
the  surface  of  the  water  at  the  point 
A,  and  from  the  points  m  and  p,  let  the  lines  m  n  and  p 
q.  be  drawn  perpendicular  to  this  line.  The  angle  n  A 
m,  is  the  angle  of  incidence,  and  the  angle  p  A  q,  is  the 
an'jle  of  refraction.  If  now  we  measure  the  lines  in  n 
and  p  q,  and  divide  the  length  of  m  n  by  that  of  p  q, 
we  will  obtain  a  quotient  which  is  called  the  index  of 
refraction. 

It  is  evident  that  if  the  beam  were  bent  still  more  at 


NATURAL    PHILOSOPHY.  199 

A,  this  quotient  would  be  larger :  the  larger  the  index 
of  refraction,  the  greater  the  refracting  power  of  the 
substance. 

For  water,  the  index  of  refraction  is  always  1.336 ;  for 
crown  glass,  the  index  is  1.58  ;  for  the  bisulphide  of  car- 
bon, it  is  1.673.  . 

(70.)  The  effects  of  lenses  are  explained  by  the  prin- 
ciples of  refraction. 

A  convex  lens  collects  the  rays  of  light  which  pass 
through  it. 

A  concave  lens  separates  the  rays  which  pass  through  it. 

1.  Lenses. — A  lens  is  a  transparent  body  bounded  by 
surfaces,  one  at  least  of  which  is  curved.  Six  different 
varieties  are  used  in  the  arts.  They  are  usually  made 
of  glass,  and  their  shapes  are  represented  by  sections 
in  Fig.  96. 

The  double  convex  lens  A ,  is  bounded  by  two  convex 
surfaces. 

The  plano-convex  B,  is  bounded  by  surfaces,  one  of 
which  is  convex  and  the  other  plane. 

Fig.  96. 


The  meniscus,  C,  has  one  surface  convex  and  the  other 
concave,  the  convexity  being  greater  than  the  concavity. 

The  double  concave  lens  D,  has  two  concave  surfaces. 

The  plano-concave  lens  E,  has  one  surface  concave  and 
the  other  plane. 


200  NATURAL    PHILOSOPHY. 

The  concavo-convex  lens  F,  has  one  surface  convex 
and  the  other  concave,  the  convex  surface  being  less 
curved  than  the  concave  surface. 

The  first  three  of  these  varieties,  A,  B,  C,  are  convex 
lenses ;  the  others,  D,  E,  F,  are  concave  lenses. 

2.  The  effect  of  convex  lenses. — By  remembering  tho 
two  laws  of  refraction,  and  that  a  radius  of  a  sphere  ia 
always  perpendicular  to  its  surface,  it  will  not  be  diffi- 
cult to  trace  the  rays  of  light  as  they  are  refracted  in 
going  through  a  lens.  Let  a  section  of  a  double  con- 
vex lens  be  represented  by  M  K",  in  Fig.  97.  Tho  two 

Fig.  97. 


curved  surfaces  are  parts  of  the  surfaces  of  two  spheres, 
who?*3  centers  are  at  C  and  C'.  The  line  CO',  drawn 
through  these  centers  of  curvature,  is  called  the  axis  of 
the  lens.  Now  suppose  two  rays  of  light,  a  b  and  c  d,  par- 
allel to  the  axis,  to  fall  upon  the  lens  at  the  points  b  and  d. 
On  entering  the  denser  medium,  they  will  be  bent  toward 
the  perpendiculars  to  the  surface  at  these  points.  These 
perpendiculars  are  the  dotted  lines  C'  b  and  C'  d.  The 
refracted  rays  in  the  lens  go  in  the  directions  b  h  and 
d  e.  On  passing  out  of  the  lens  into  air,  they  are  bent 
from  the  perpendiculars  to  the  surface  at  the  points  h 
and  e.  These  perpendiculars  are  the  lines  0  h  and 
0  e,  and  the  refracted  rays  cross  each  other  at  tho 
point  C  .  Parallel  rays  refracted  by  a  convex  lens  are 


NATURAL    PHILOSOPHY.  2Q1 

made  converging.  And  we  should  find  that  in  all  cases, 
the  rajs  after  refraction  will  be  nearer  to  each  other 
than  before.  The  general  effect  of  the  convex  lens  is 
to  collect  rajs  of  light. 

The  plano-convex  lens  and  the  meniscus  will  have  the 
•ame  effect,  but  in  a  less  degree. 

The  point  C'  is  the  principal  focus  of  the  lens:  it  w 
the  focus  of  rays  which  are  parallel  to  the  axis.  The 
distance  of  this  point  from  the  lens  will  depend  upon 
the  curvature  of  the  lens,  and  upon  the  index  of  re- 
fraction. If  the  two  surfaces  of  the  lens  are  equally 
curved,  and  it  be  made  of  glass  whose  index  of  refrac- 
tion is  1.5°,  then  the  principal  focus  will  be  at  the  center 
of  curvature,  as  in  Fig.  97. 

3.  The  effect  of  concave  lenses. — That  concave  lenses 
separate  rays  of  light,  may  be  shown  by  tracing  the 
rays  represented  in  Fig.  98. 

Fig.  98. 


Let  M  N  represent  the  double  concave  lens,  whose 
centers  of  curvature  are  C  and  C.  Two  rays  of  light, 
parallel  to  the  axis,  striking  the  lens  at  the  points  I 
and  d,  will  be  bent  toward  the  perpendiculars,  and  pass 
through  the  glass  in  the  direction  b  h  and  d  e.  On 
emerging,  they  will  be  bent  from  the  perpendicular,  and 
go  in  the  directions  h  Ic  and  e  m.  We  thus  find  that 
parallel  rays  are  made  diverging.  Diverging  rays 

9* 


NATURAL    PHILOSOPHY. 

would  be  made  more  diverging,  while  converging  raja 
would  be  made  less  converging.  In  all  cases,  rays  re- 
fracted by  a  double  concave  lens  would  be  separated, 

The  plano-concave  lens,  and  the  concavo-convex  lena 
have  the  same  effect,  but  in  a  less  degree. 

(71.)  If  an  object  be  placed  in  front  of  a  convex  lens, 
an  image  of  it  will  be  formed  on  the  other  side  of  the 
lens.  To  explain  this,  remember  that  the  image  of  any 
point  will  be  made  where  rays  of  light  going  from  it, 
either  meet,  or  appear  to  meet,  after  refraction. 

1.  linages  are  formed. — If  a  convex  spectacle  glass  is 
held  in  front  of  a  window,  at  some  distance,  and  a  sheet 
of  white  paper  is  put  in  front  of  it,  the  light  from  the 
window  will  go  through  the  glass  and  fall  upon  the- 
paper.     If  the  distance  from  the  glass  to  the  paper  be 
just  right,  a  very  small  but   very  perfect   image   or 
picture  of  the  window  will  be  seen  upon  it. 

If  a  good  double  convex  lens,  three  or  four  inches  in 
diameter  be  at  hand,  a  very  beautiful  experiment  may 
be  made.  Through  an  opening  in  a  shutter  of  a  dark- 
ened room,  admit  ar  beam  of  sunlight.  Into  this  beam 
put  any  small,  transparent  object,  it  may  be  a  picture 
painted  on  glass,  or,  quite  as  well,  a  wing  of  the  dragon- 
fly, so  that  the  light  may  pass  through  it.  If  now,  the 
lens  be  moved  back  and  forth  in  front  of  this  object, 
until  just  the  right  distance  is  found,  a  very  large  and 
perfect  image  will  be  seen  inverted  upon  the  opposite 
wall  of  the  room. 

2.  The  images  of  points. — Now  let  us  see  how  these 
beautiful  effects  are  produced. 

Suppose  an  arrow  N  S  (Fig.  99),  placed  at  some 
distance  in  frcnt  of  a  convex  lens  M,  whose  centers  of 


NATURAL     PHILOSOPHY.  203 

curvature  are/  and//  Two  rays  of  light  from  the 
point  N,  passing  through  the  lens,  will  be  refracted  eo 
as  to  cross  each  other  at  the  point  n.  This  point  where 


F.g.  99. 


rays  of  light  meet  after  refraction,  is  ike  image  of  the 
point  N,  from  which  they  came.  The  rays  from  the 
point  S  of  the  object,  after  refraction,  cross  each  other 
at  s,  and  form  an  image  there.  From  points  between 
IS"  and  S,  rays  of  light  going  through  the  lens  will  be 
collected  on  corresponding  points  between  n  and  s,  and 
thus  a  perfect  image  will  be  made  inverted  at  n  8. 

In  this  way,  it  is  easy,  by  a  diagram,  to  illustrate  the 
formation  of  all  images  by  lenses. 

(72.)  If  an  object  be  placed  at  a  point  twice  the  focal 
distance  from  a  convex  lens,  an  image  of  it  will  be  formed 
at  an  equal  distance  on  the  other  side.  If  the  object  be 
moved  farther  away,  or  nearer  to  the  lens,  the  position 
and  s^ze  of  the  image  will  be  changed. 

1.  The  object  twice  the  focal  distance. — Suppose  the 
lens  to  be  one  whose  focus  is  at  the  center  of  curvature, 
and  that  the  object  is  just  twice  that  distance  from  the 
lens,  as  shown  by  the  arrow  N  S  (Fig.  100).  Two  rays 
of  light  from  the  top  of  the  arrow  go  through  the  lens, 
bending  according  to  the  laws  of  refraction,  and  cross 
each  other  at  the  point  n.  Two  rays  from  the  bottom 


204  NATURAL    PHILOSOPHY. 

of  the  arrow  go  through  the  lens  and  cross  each  other 
at  the  point  s.  Join  the  points  n  and  s,  and  n  s  repre- 
sents the  image  that  is  formed.  This  image  will  be  at 


.  100. 


twice  the  focal  distance  on  the  other  side  of  the  lens,  of 
the  same  size  as  the  object,  and  inverte  1 

2.  The  object  farther  away. — This  case  is  represented 
bj  Fig.  99.     Suppose  that  in  front  of  the  lens  M,  an 
arrow,  with  its  head  downward,  represented  by  n  *,  is 
placed  at  more  than  twice  the  focal  distance  from  the 
lens.     Two  rays  from  the  arrow-head,  after  refraction, 
will  be  found  to  cross  each  other  at  ~N  ;  two  rays  from 
8  will,  after  refraction,  cross  each  other  at  S.      The 
image  N  S,  is  on  the  other  side  of  the  lens,  at  a  less 
distance,  smaller  than  the  object,  and  inverted. 

3.  The  object  at  a  less  distance. — If,  in  Fig.  99,  we 
suppose  1ST  S  to  represent  the  object,  outside  the  focus, 
but  at  less  than  twice  the  focal  distance,  its  image  will 
be  found  at  n  s.     In  this  case  the  image  will  be  at  a 
greater  distance  on  the  other  side  of  the  lens,  larger  than 
the  object  and  inverted. 

4.  The  object  between  the  focus  and  the  lens. — One 
more  case  remains  to  be  considered.     Suppose  the  ob- 
ject to  be  between  the  focus  and  the  lens.     Let  M  N 
(Fig.  101),  represent  a  lens  whose  focus  is  at  C,  and  let 
the  object  A  B,  be  placed  between  this  point  and  the 
lens.     An  attentive  examination  of  the  figure;,  show 


NATURAL     PHILOSOPHY. 


205 


that  the  rays  of  light  from  the  point  A,  are  diverging 

after  refraction.     And  since  they  can  never  meet,  it  is 

clear      that      no  Fig.  101. 

image      can      be 

formed     on     that 

side  of  the   lens, 

but  if  an  eye  at  E, 

receive  these  rays 

they  will  produce 

the  same  effect  as 

if  they  came  from   A'.      In   like   manner,   the   rays 

from   B,  entering  the  eye  at   E,    will  seem   to   have 

come  from  B'.    Hence  an  image  will  seem  to  be  formed 

at     '  B'.     This  image  will  be  on  the  same  side  of  the 

lens  as  the  object,  erect,  and  larger  than  the  object. 

(73.)  Images  are  also  formed  by  concave  lenses. 
They  are  on  the  same  side  as  the  object,  smaller,  and 
erect. 

1.  Suppose  an  object  A  B  (Fig.  102),  in  front  of  a 

Fig.  102. 


concave  lens  M  N.  Rays  of  light  from  A,  after  refrac- 
tion, diverge  as  if  they  had  come  from  a ;  rays  from  B, 
after  refraction,  diverge  as  if  they  had  come  from  b ;  the 
image  will  thus  appear  to  be  made  at  a  b.  This  image 


206  NATURAL    PHILOSOPHY. 

is  on  the  same  side  of  the  lens,  smaller  than  the  object^ 
and  erect. 


§   4.    ON    THE    DECOMPOSITION     OF    LIGHT. 

(74.)  Prisms  refract  light;  they  also  decompose  it. 
They  separate  white  light  into  rays  of  seven  different 
colors,  viz. :  violet,  indigo,  blue,  green,  yellow,  orange, 
and  red. 

1.  Prisms. — Any  transparent  body,  two   of  whose 
sides  are  inclined  toward  each  other,  is  a  prism.     The 
most  common  form  of  the  prism  is  a  triangular  piece  of 
glass.     A  water  prism  may 'be  made  by  taking  a  three- 
cornered  vessel,  with  glass  sides,  and   filling   it  with 
water.     Other  fluids  may  be  used  in  place  of  water. 

2.  Prisms  refract  light. — Light,  in  passing  through 
prisms,  must  obey  the  laws  of  refraction.     In  Fig.  103, 

Fig.  103. 


the  triangle  m  n  o,  represents  a  section  of  a  prism.     A 
ray  of  light  striking  its  surface  at  #,  will  be  bent  to- 


NATURAL    PHILOSOPHY. 


207 


ward  a  perpendicular  on  entering,  and  from  a  perpen- 
dicular on  emerging,  finally  taking  the  direction  b  c. 
To  the  eye  at  <?,  this  light  would  seem  to  come  from  the 
object  at  r  instead  of  L. 

3.  Prisms  decompose  light. — The  white  light  that 
comes  from  the  sun,  or  from  other  luminous  bodies,  is 
really  made  up  of  seven  different  kinds  of  light.  The 
way  in  which  Sir  Isaac  Newton  made  this  great  dis- 
covery is  shown  in  Fig.  104.  In  the  window-shutter 
S,  of  a  darkened  room,  he  made  a  small  hole,  and 


Fig.  104. 


placed  behind  it  a  prism,  A.  B  C,  so  that  the  beam  of 
sunlight  D  could  fall  obliquely  upon  one  of  its  sides  at 
E.  Were  it  not  for  the  prism  the  beam  of  light  would 
go  straight  forward  to  F,  where  it  would  make  a  round 
white  spot,  but  being  refracted  by  the  prism,  it  formed 
above  F,  upon  the  screen  M,  an  oblong  image  contain- 
ing seven  different  colors.  These  colors  appeared  in 
order  from  the  top  of  the  image,  violet,  indigo,  blue, 
green,  yellow,  orange,  and  red. 

These  colors  are  separated,  it  seems,  because  the 
prism  has  power  to  bend  some  of  them  more  than 
others.  The  violet  rays  are  bent  most ;  the  red  rays 
least 


208  NATURAL    PHILOSOPHY. 

The  oblong  image  upon  the  screen  is  called  the  solar 
spectrum.  The  power  of  a  prism  to  separate  the  color 
of  white  light  is  called  dispersive  power. 

The  prism  in  this  way  enables  us  to  analyze  white 
light,  or  to  find  out  the  colors  of  which  it  is  made ; 
and  now,  if  by  any  means  we  can  unite  those  seven 
colors,  we  shall  produce  white  light  again.  This  can 
be  d'one  by  using  any  instrument  which  collects  rays  of 
light.  If  the  rays  fall  upon  a  concave  mirror,  they  will 
be  reflected  to  a  focus,  which  will  be  a  white  spot.  If 
the  rays  are  received  upon  a  double  convex  lens,  they 
will  be  refracted  to  a  focus,  and  this  focus  will  be  also 
white.  Sir  Isaac  Newton  collected  the  rays  by  using  a 
second  prism,  exactly  like  the  first,  but  placed  beside 
it  so  as  to  bend  the  rays  in  the  opposite  direction  :  the 
image  on  the  screen  was  white. 

(75.)  The  spectrum  formed  by  sunlight  or  by  star- 
light is  crossed  by  a  great  many  fine  black  lines,  while 
the  spectra  formed  by  light  from  artificial  sources,  are 
crossed  by  different  colored  bright  lines. 

1.  The  Hack  lines. — The  whole  length  of  the  solar 
spectrum,  when  seen  by  the  naked  eye,  seems  to  be 
colored,  but  when  seen  through  a  magnifying  glass,  a 
great  many  fine  black  lines  are  found  to  cross  it,  as  if  a 
delicate  brush,  dipped  in  the  purest  black,  had  been 
drawn  across  it  by  a  skillful  artist.  A  beam  of  sun- 
light always  gives  the  same  set  of  lines,  holding  the 
game  relative  position  in  the  spectrum.  A  beam  of 
starlight  gives  a  different  set,  and  the  light  from  dif- 
ferent stars  gives  each  a  set  of  its  own.  These  lines  are 
usually  called  Fraunhofer's  lines,  in  honor  of  him  who 
first  examined  them  carefully. 


NATURAL    PHILOSOPHY.  208 

2.  The  bright  lines. — When  the  light  from  an  arti- 
ficial source  is  passed  through  a  prism  and  its  spec- 
trum is  seen  through  a  magnifying  glass,  no  black  lines 
are  visible,  but  instead  of  these,  there  will  be  seen  lines 
of  exceeding  brightness,  and  of  different  colors.  The 
color  of  these  lines,  and  their  place  in  the  spectrum, 
will  depend  upon  the  substance  whose  flame  gives  the 
light.  If,  for  example,  a  little  common  salt  be  burned 
in  a  hot  gas  flame,  two  yellow  lines  of  surprising 
brightness  will  always  appear  in  the  yellow  part 
of  the  spectrum,  while  the  metal  potassium  in  the 
flame  will  always  give  two  lines,  one  of  a  brilliant 
crimson  color,  in  the  red  end  of  the  spectrum,  the  other 
a  beautiful  blue  line  away  off  in  the  violet  end.  Each 
substance  gives  a  set  peculiar  to  itself. 

(76.)  Drops  of  rain  may  decompose  the  sunlight :  in 
this  way  the  rainbow  is  produced.  The  primary  bow 
consists  of  bands  of  the  seven  colors  of  the  spectrum, 
arranged  in  parallel  arches,  with  the  red  band  on  the 
outside. 

In  the  secondary  bow  the  order  of  the  colored  arches 
is  changed,  the  violet  being  on  the  outside. 

1.    The    primary  Fig.  105. 

rainbow. — This  most 
beautiful  phenome- 
non is  produced  by  the 
action  of  rain  drops  ; 
they  decompose  the 
sunlight  and  send  its 
rich  colors  to  the  eye. 

To  understand  this 
action,   suppose    the 


210  NATURAL     PHILOSOPHY. 

circle,  whose  center  is  at  C  (Fig.  105),  to  represent  a 
section  of  a  drop  of  water.  Rajs  of  sunlight  (S  A)  fall- 
ing upon  the  upper  part  of  the  drop  will  be  refracted 
to  the  point  B.  At  this  point  a  part  of  the  light 
will  pass  out  into  the  air  again,  but  another  part  will  be 
reflected  by  the  inner  surface  of  the  water  and  strike 
the  surface  at  another  point,  D.  The  light  which 
here  goes  out  of  the  drop  into  the  air,  will  be  again 
refracted.  Xow  the  light  will  not  only  be  refracted, 
in  its  passage  through  the  drop ;  it  will  be,  at  the  same 
time  decomposed.  On  coming  out  of  the  water  the 
red  ray,  bent  least,  will  take  a  direction  represented 
by  D  E  ;  the  violet  ray,  bent  most,  may  be  represented 
by  D  V ;  and  all  the  other  colors  of  the  spectrum  will 
be  found  between  these. 

2.  TJie  red  land  on  the  outside. — Now  it  is  quite 
clear  that  if  the  person  were  standing  upon  the  ground 
in  the  direction  of  D  E,  so  that  the  red  rays  from  this 
drop  would  enter  his  eye,  the  violet  rays,  and  indeed 
all  the  other  colors,  would  'go  over  his  head.  To  him 
this  drop  of  water  would  appear  red.  Another  drop, 
some  distance  below  this  one,  would  send  violet  rays 
into  the  same  eve.  Between  the  drop  which  sends  the 
red,  and  that  which  sends  the  violet,  there  would  be 
Fig.  ice.  others  from  which  the 

eye  would  receive  the 
other  colors  of  the  spec- 
trum. (Fig.  106.) 

Hence,  when  a  show- 
er of  rain  is  falling,  and 
the  sun  is  at  the  same 
time  shining  in  the  op 
posite  part  of  the  sky, 


NATURAL     PHILOSOPHY. 

so  that  a  person  looking  toward  the  shower,  will  have 
his  back  turned  toward  the  sun,  he  will  see  the  seven 
colors  of  the  spectrum  painted  upon  the  cloud  in  order, 
with  red  at  the  top  and  violet  at  the  bottom. 

3.  The  colors  are  in  the  form  of  an  arch. — Now, 
suppose  a  line  drawn  from  the  sun  through  the  eye  of 
the  observer,  and  straight  onward  until  it  reaches  a 
point  O  (Fig.  105),  directly  under  the  drop  C,  which 
sends  the  light  to  the  eye.     If  this  drop  sends  a  red 
ray  to  the  eye,  then   all  others,  which  like   this   are 
opposite  the  sun,  and  whose  distance  from  O  is   the 
same,  will  also  give  red  rays.     If  the  arc  of  a  circum- 
ference be  drawn  with  O  as  a  center,  and  with  a  radius 
C  O,  all  drops  along  this  circumference  will  be  equally 
distant  from  the  center  O,  and  will  therefore  give  red 
rays.     The  red  part  of  the  rain~bow  is,  for  this  reason,  a 
circular  arch,  and  for  the  same  reason,  the  other  colors 
are  parallel  arches  below  the  red. 

4.  The  secondary  bow. — Outside   of  the    bow  just 
explained,  another,  the  secondary  bow  is  often  seen. 
Its  colors  are  more  dim,  and  their  order  is  reversed, 
the  violet  being  at  the  top  and  the  red  at  the  bottom. 

To  explain  the  primary  bow  we  trace  rays  of  light 
falling  upon  the  top  of  the  drops  of  water.  But  drops 
of  rain  in  the  air  are  entirely  covered  with  light,  and 
to  explain  the  secondary 
bow,  we  may  trace  the  rays 
which  fall  upon  their  lower 
parts.  The  diagram  (Fig. 
107)  illustrates  this.  A 
beam  of  light  S  A,  re- 
fracted  on  entering  the 
drop,  goes  through  to  its 


212  NATURAL    PHILOSOPHY. 

inner  surface  at  B,  from  which  it  is  reflected.  It 
strikes  the  inner  surface  again  at  D,  and  is  again 
reflected.  At  the  point  F,  a  part  of  the  beam  will 
be  again  reflected,  but  another  part  will  pass  out  into 
the  air  and  be  bent  downward.  In  its  passage  through 
the  drop  the  light  is  not  only  refracted ;  it  is  decom- 
posed. If  F  G  represents  the  red  ray,  then  F  Y  may 
represent  the  violet  "ray.  Now,  clearly,  if  the  red  ray 
enters  the  eye,  the  other  colors  will  fall  below  it,  so 
that  this  drop  will  appear  red.  Other  drops  above 
this  one  will  give  the  other  colors  in  their  order.  Hence 
the  outside  band  of  the  secondary  bow  will  be  violet, 
the  inner  one  red. 

(77.)  Bodies  are  of  different  colors,  only  because 
they  decompose  the  sunlight,  and  reflect  different 
parts  of  it  to  the  eye.  The  various  colors  of  the 
sky,  and  the  clouds,  are  due  to  the  decomposition 
of  the  light  which  comes  through  them  from  the 
sun. 

1.  The  color  of  bodies. — The  sun  sheds  a  flood  of 
pure  white  light  upon  all  bodies  alike.  This  white 
light  is  decomposed  at  their  surfaces.  Some  of  its 
colors  are  transmitted  or  absorbed  by  the  body,  while 
the  others  are  reflected  to  the  eye.  One  body  is  red 
because  it  decomposes  the  sunlight  and  reflects  the  red 
rays ;  another  is  blue,  because  it  reflects  only  blue  rays. 
The  foliage  of  trees  in  the  spring-time,  receives  the 
Bun's  white  light,  decomposes  it,  and  reflects  onlj  the 
green  rays.  The  petals  of  the  violet  decompose  the 
sunlight  to  share  with  us  the  beautiful  colors  of  the 
spectrum ;  it  reflects  the  colors  of  the  violet  end,  and 
keeps  to  itself  those  of  the  other.  A  body  whfcb 


NATURAL    PHILOSOPHY.  213 

reflects  all  the  color  of  the  light  it  receives  is  white; 
one  which  reflects  none  is  black. 

2.  The  color  of  the  sky. — The  sky,  when  free  from 
clouds,  is  blue,  because  the  particles  of  the  atmosphere 
reflect  blue  rays  of  light.     If  the  thin  air  could  not  re- 
flect light  at  all,  the  sky  would  appear  black :  if  it 
reflected  it  without  decomposition  it  would  be  white. 
The  white  sunlight  falls  upon  its  molecules,  is  decom- 
posed by  them,  and  only  those  rays  which  make  up  the 
delicate  blue  color  of  the  sky  are  reflected  to  our  eyes. 

3.  The  color  of  the  clouds. — The  clouds  both  reflect 
and  refract  the  sunlight,  and  all  their  varied  colors  are 
due  to  the  decomposition  thus  produced.    There  can  be 
no  more  gorgeous  display  of  colors  than  we  often  see 
upoa  the  clouds  of  the  morning  and  the  evening  sky. 
What  grand  and  diversified  effects  to  be  produced  by 
means  of  such  simple  materials  as  light,  water,  and  air  I 

§    5.    ON    OPTICAL   INSTRUMENTS. 

(78.)  The  microscope,  the  telescope,  and  many  other 
instruments,  help  the  eye  to  see  small  or  distant  objects, 
by  forming  large  and  perfect  images  of  them  nearby, 
for  it  to  examine. 

The  eye  itself  is  an  optical  instrument  of  the  most 
perfect  construction. 

1.  The  microscope. — The  simple  microscope  consists 
of  a  single  convex  lens.  The  lens  is  held  in  the  hand 
at  a  little  less  than  its  focal  distance  from  the  object. 
The  eye  receives  the  light  which  comes  from  the  object 
through  the  glass,  and  sees  a  magnified  image  en  the 
other  side. 

The  operation  of  the  compound  microscope  may  be 


NATURAL   PHILOSOPHY 


understood  by  means  of  a  diagram  (Fig.   108).     Two 
convex  lenses,  and  sometimes  three,  are  used. 


Fig.  108. 


The  lens  A,  called  the  object-glass,  refracts  the  light 
from  the  object  O,  placed  a  little  beyond  its'  focus,  and 
forms  an  image  inverted  at  O'.  The  light  from  this 
image  is  refracted  by  another  lens  B,  caRed  the  eye- 
glass, and  if  the  rays  are  received  into  the  eye,  they  will 
appear  to  have  come  from  C  D,  which  is  the  magnified 
image  of  the  object. 

By  means  of  this  instrument,  things  otherwise  too 
small  to  be  seen,  are  made  visible,  and  a  world  of 
wonderful  creations  is  thus  revealed  for  the  study  and 
admiration  of  man.  A  drop  of  water  from  a  stagnant 
pool,  is  found,  by  means  of  the  microscope,  to  be  swarm 
ing  with  living  creatures,  whose  forms  are  as  perfect, 
and  whose  appetites  are  not  unlike  those  of  larger 
animals. 

2.  The  telescope. — A  telescope  is  ased  for  viewing 
distant  objects.  Sometimes  a  lens  is  employed  to  form 
an  image;  sometimes  the  image  is  formed  by  a  mirror, 
Tn  the  first  case,  the  instrument  is  called  a  refracting 
telescope  j  in  the  second,  it  is  called  a  reflecting  telescope. 

Of  the  refracting  telescope  there  are  three  important 
forms :  Galileo's^  the  astronomical,  and  the  terrestrial. 


NATURAL    PHILOSOPHY. 


215 


In  Galileo's  telescope  there  is  a  double  convex  object- 
glass  M  N  (Fig.  109),  and  a  double  concave  eye-glass, 


E  F.  Rays  of  light  from  the  point  A  of  a  distant  object 
A  B,  after  passing  through  the  two  glasses,  diverge  as 
if  they  came  from  the  point  a,  while  rays  from  the  point 
B  of  the  object  after  refraction,  diverge  as  if  from  the 
point  b.  An  erect  image  a  Z>,  will  be  seen  by  holding 
the  eye  in  front  of  the  eye-glass  E. 

The  opera-glass  consists  of  two  small  galilean  tele- 
scopes placed  side  by  side. 

In  the  astronomical  telescope,  two  double  convex 
lenses  are  used.  The  object-glass  O  (Fig.  110),  forms  a 

Fig.  110. 


small   image  a  b  of   a  distant  object  A  B.     The   eye- 
glass (E)  being  so  placed  that  its  focus  (F)  is  a  little 


216  NATURAL    PHILOSOPHY. 

beyond  this  image,  refracts  the  light,  so  that  it  will 
appear  to  have  come  from  a  magnified  image  c  d.  The 
course  of  the  rays  may  be  traced  in  the  figure.  In 
this  instrument  the  image  is  always  inverted. 

The  terrestrial  telescope  is  used  for  viewing  distant 
objects  upon  the  earth.  To  see  them  upside  down, 
as  in  the  astronomical  telescope,  is  not  desirable: 
that  they  may  be  seen  right  side  up,  two  convex 
lenses  are  placed  between  the  object-glass  and  the 
eye-glass.  The  arrangement  of  the  glasses,  and  the 

Fig.  111. 


course  of  the  rays,  are  shown  in  Fig.  111.  The 
object-glass  O,  forms  a  small  inverted  image  T,  of 
a  distant  object  A  B,  near  its  focus.  From  this 
image  the  light  goes  through  the  two  lenses,  m  and  /i, 
to  form  a  second  image  L.  This  image  is  erect  with 
respect  to  the  object,  and  it  is  magnified  by  the  eye- 
glass E,  in  the  usual  manner. 

Of  the  reflecting  telescope  there  are  several  va- 
rieties. In  all  of  them  the  image  of  a  distant  object 
is  formed  by  a  concave  mirror,  and  this  image  is 
magnified  by  a  convex  eye-glass. 

In  the  Herschelian  telescope  (Fig.  112),  the  mirror 
M  K  is  inclined  to  the  axis  of  the  tube  in  which  it 
is  placed,  so  that  rays  of  light  from  a  distant  object 
will  be  reflected  to  a  focus  near  to  one  side  of  the 


NATURAL    PHILOSOPHY. 


217 


tube  at  the  other  end.  The  observer,  looking  down 
into  the  tube,  holds  an  eye-piece,  #,  in  his  hand, 
through  which  he  views  a  magnified  image. 

Fig.  112. 


3.  The  magic  lantern. — The  magic  lantern  is  an  in- 
strument by  which  the  image  of  a  small  transparent 
picture,  painted  on  glass,  may  be  thrown  upon  a  screen, 
so  much  magnified  that  a  whole  audience  may  see  it. 

It  consists  of  a  powerful  lens,  with  objects  highly  il- 
luminated by  lamp-light  placed  so  near  it,  that  their 
images  are  formed  far  away.  Fig.  113  shows  a  sec- 
tion of  the  instrument.  Inside  of  a  dark  box,  a  strong 

Fig.  113. 


light  (L)  is  placed.  Behind  this  light  is  a  concave 
mirror  (M)  and  in  front  of  it  a  convex  lens  A.  This  lens 
is  at  the  entrance  of  a  tube  which  projects  from  the 
side  of  the  box.  Inside  this  tube  slides  a  smaller  one* 
10 


218 


NATURAL    PHILOSOPHY. 


in  which  is  fixed  another  powerful  lens.  The  picture 
is  placed  in  a  slit  C,  provided  for  it  in  the  larger  tube, 
just  in  front  of  the  first  lens.  The  lamp  fills  the  box 
with  a  strong  light.  The  lens  A,  receiving  light  di- 
rectly from  the  lamp,  and  reflected  from  the  mirror, 
condenses  it  upon  the  object  and  highly  illuminates  it. 
The  light  from  this  bright  object  goes  on  through  the 
second  lens  to  the  distant  screen,  and  there  forms  a  large 
and  perfect  image. 

This  instrument  is  very  useful  to  the  lecturer  or  the 
teacher,  who  would  illustrate  the  wonderful  phenomena 
of  nature.  By  means  of  small  pictures,  or  of  small 
transparent  objects,  he  is  able  to  make  hia  audience 
see  the  relations  of  the  heavenly  bodies  taught  in 
Astronomy,  or  the  delicate  phenomena  desc^bed  in 
Natural  Philosophy  and  Chemistry. 

4.  The  camera  obscura. — The  camera  obscai*  is  an 
instrument  by  which  to  form  miniature  images  rf  ob- 
jects. It  consists  of  a  dark  box,  a  section  of  whi^h  is 
represented  by  A  B  (Fig.  114),  containing  a  scree*  S, 

Fig.  114. 


and  having  a  double  convex  lens  L,  filling  an  opening 
in  one  end.  The  distance  of  the  lens  from  the  screen 
may  be  varied  by  sliding  the  tube  which  carries  it  back 
and  forth  in  the  larger  tube  C.  The  light  from  the 
object  O  is  refracted  by  the  lens,  and  a  beautiful  image 


NATURAL    PHILOSOPHY.  219 

vri]l  be  formed  upon  the  screen.     This  image  is  always 
inverted,  and  smaller  than  the  object. 

The  camera  may  be  illustrated  by  a  very  simple  ex- 
periment. If,  in  a  hole  in  the  shutter  of  a  darkened 
room,  is  placed  a  double  convex  lens,  the  room  is  itself 
a  camera  obscura,  and  persons  present  may  see  what 
takes  place  inside.  Let  a  white  sheet  be  hung  in  front 
of  the  lens  at  a  proper  distance,  and  it  is  at  once  cov- 
ered with  a  perfect  picture  of  whatever  scenery  may  be 
outside.  Houses  and  distant  hills;  the  sky  with  its 
floating  clouds:  men  and  a^mals  in  the  street,  and 
even  the  flying  oirds,  and  the  curling  smoke,  are  paint- 
ed upon  the  screen,  with  colors  taken  from  the  sun's 
bright  rays. 

5.  The  eye. — But  most  perfect  of  all  optical  instru- 
ments, is  the  eye.  Who  could  at  first  believe,  that  in 
describing,  as  we  have  done,  the  camera  obscura,  we 
were  describing  a  rougli  model  of  the  human  eye ! 
Yet  the  eye  is  nothing  but  a  simple  camera  obscura, 
differing  from  it  only  in  its  wonderful  perfection. 

The  human  eye  is  a  globular  chamber,  having  for  its 
outer  wall  a  hard  tough  membrane  called  the  sclerotic 
coat.  The  front  part  of  the  sclerotic  coat  is  a  trans- 
parent substance  called  the  cornea.  The  chamber  is 
lined  with  a  more  delicate  membrane  called  the  cJioroid, 
arid  to  insure  the  darkness  of  the  place,  this  is  covered 
upon  the  inside  with  a  Hack  paint.  The  front  part  of 
the  choroid  coat  is  called  the  iris,  and  in  the  center  of 
this  is  a  round  hole  called  the  pupil  of  the  eye,  through 
which  light  may  pass  into  the  dark  chamber  beyonl 
Behind  this  opening,  is  a  double  convex  lens,  very 
transparent  and  considerably  hard,  called  the  crystal- 
line lens.  Between  this  lens  and  the  cornea  is  a  limpid 


220  NATURAL    PHILOSOPHY. 

liquid  called  the  aqueous  humor,  and  filling  the  dark 
chamber,  behind  the  lens,  is  another  fluid,  called  the 
vitreous  humor.  The  arrangment  of  these  parts  may 
be  understood  by  attentively  studying  Fig.  115,  which 


Fig,  11& 


represents  a  section  of  the  eye.  S  S,  is  the  outer  or 
sclerotic  coat,  sometimes  called  the  white  of  the  eye. 
C  C,  is  the  cornea ;  it  is  more  convex  than  the  sclerotic. 
K  K,  is  the  choroid,  and  i  i,  is  the  iris,  the  vertical 
curtain  which  shuts  out  all  light,  except  what  may  get 
through  the  hole  at  its  center — the  pupil.  L  L,  is  the 
crystalline  lens,  and  the  large  chamber  Y,  is  filled 
with  the  vitreous  humor.  The  course  of  the  rays  of 
light  is  also  shown  in  the  figure.  An  inverted  image 
of  an  object  O,  is  formed  at  R.  It  is  there  received 
upon  a  net-work  of  delicate  nerve  fibers  called  the 
retina,  ~R  R.  The  mind  takes  cognizance  of  this  pic- 
ture, and  the  person  is  said  to  see  tJie  object  O.  These 
pictures  on  the  retina  are  always  smaller  than  the  ob- 
jects, and  the  more  distant  the  object,  the  more  minute 
the  image.  The  diameter  of  the  eye  is  little  more  than 
an  inch,  and  yet  when  a  person  sees  an  extended  land- 


NATURAL    PHILOSOPHY.  223 

scape,  every  visible  object,  far  and  near,  is  painted 
upon  the  inner  lining.  If  the  picture  in  the  human 
eye  be  thus  minute,  what  must  it  be  in  the  eye  oi  • 
canarv-bird  or  butterfly  1 


NATUKAL     PHILOSOPHY. 


CHAPTEK    VII. 


MODES  OF  VIBRATION.— ni.  HEAT. 

§   1.    OF  THE   SOURCES   AND   NATURE   OF   HEAT. 

(T9.)  THE  sources  of  heat  may  be  studied  in  three 
groups.  First,  the  heavenly  bodies ;  second,  mechani- 
cal action ;  and  third,  chemical  action. 

I. — THE    HEAVENLY    BODIES. 

A. — The  sun  and  the  stars  are  sources  of  heat. 

1.  The  sun. — Floods  of  heat  come  down  with  the 
sunlight.     Upon  this  most  familiar  fact  we  need  not 
dwell,  further  than  to  notice  that  the  amount  of  heat 
received  from  the  sun  is  doubtless  greater  than  from 
any  other  source,  and  that  as  this  amount  varies  from 
month  to  month,  it  allows  the  earth  to  be  clothed  in 
the  snows  of  winter,  the  verdure  of  spring,  the  ma- 
turing growths  of  summer,  and  the  ripening  fruits  of 
autumn. 

2.  The  stars. — Heat  comes  with  the  starlight  as  well 
as  with  the  sunlight.     During  the  night  when  the  stars 
are  seen,  not  more  than  during  the  day  when   the 
stronger  light  of  the  sun  obscures  them,  each  star  is 
sending  its  proportion  of  heat  to  warm  the  earth. 


NATURAL     PHILOSOPHY.  -223 


H. — MECHANICAL    ACTION. 

B.— No  mechanical  action  can  occur  without  evofr 
ing  heat  in  the  bodies  which  act  upon  each  other. 

1.  Mechanical  action  evolves  heat. — When  the  savage 
lights  his  fire  by  rubbing  two  pieces  of  hard  wood  to- 
gether, he  produces  heat  by  friction.     When  by  re- 
peated blows  of  a  hammer,  a  nail  is  made  too  hot  tc 

handle,  or  when  the  iron-clad  hoof  of  a  horse  u  strikes 
fire  "  against  a  pavement  stone,  heat  is  evolved  by  per- 
cussion.  And  finally,  when  a  piece  of  cold  wood  is 
heated  by  being  squeezed  between  the  plates  of  a  hy- 
drostatic press,  heat  is  evolved  by  pressure.  No  two 
bodies  can  act  upon  each  other,  either  by  friction,  by 
blows,  or  by  sudden  pressure  without  evolving  heat. 

2.  friction. — By  friction  heat  may  be  evolved   in 
large  quantities.     Count  Rumford  caused  18}lbs.  of 
water — almost  two  gallons,  to  boil  by  the  friction  of  a 
solid  plunger  against  the  bottom  of  an  iron  cylinder  im- 
mersed in  the  fluid.     All  bodies,  whether  solid,  liquid, 
or  gaseous,  give  off  heat  by  friction.     Sir  Humphrey 
Davy  quickly  melted  two  pieces  of  ice  by  simply  rub- 
bing them  together  in  a  room  whose  temperature  was 
below  the  freezing  point.     A  bullet  is  warmed  by  the 
friction  of  the  air  through  which  it  passes.     A  stream 
of  water  is  warmed  by  friction  against  the  sides  of  a 
channel  through  which  it  swiftly  runs.     Moreover,  the 
production  of  heat  by  friction  is  unlimited;  it  will  con- 
tinue just  as  long  as  the  friction  is  kepi  up. 

HI. — CHEMICAL     ACTION. 

C. — Chemical  action  a  source  of  heat. — Combustion 


224  NATURAL    PHILOSOPHY. 

is  the  most  familiar  form  of  chemical  action  ;  it  is  at  the 
same  time  the  most  common  source  of  artificial  heat 
"Wood  burns  in  the  stove,  or  coal  in  the  grate,  and  our 
houses  are  warmed  by  the  heat  given  off  by  this  chem- 
ical action.  A  chemical  action  takes  place  in  the  body 
of  a  person  by  which  the  food  is  changed  to  blood,  and 
the  blood  again  to  bone  and  muscle :  heat  is  evolved  by 
this  chemical  action,  which  keeps  up  the  constant  tem- 
perature of  the  body.  It  is  thought  that  no  chemical 
action  can  take  place  without  producing  heat. 

(80.)  The  material  theory  of  heat  supposes  it  to  be  a 
very  subtile  fluid  which  fills  the  spaces  between  the 
molecules  of  bodies,  and  whose  presence  in  larger  or 
smaller  quantities  constitutes  heat  or  cold. 

The  dynamic  theory  supposes  that  heat  is  a  kind 
of  vibration  among  the  molecules  of  a  body  :  the  more 
rapid  the  vibration,  the  higher  the  temperature. 

1.  The  material  theory. — The  material  theory  sup- 
poses matter  to  consist  of  molecules,  that  these  mole- 
cules do  not  touch  each  other,  and  that  the  space 
between  them  is  filled  by  a  substance  called  caloric, 
whose  molecules  are  very  much  smaller  than  those  of 
the  body.  Just  as  when  water  is  poured  into  a  barrel 
already  filled  with  bullets,  it  runs  into  the  spaces  be- 
tween them,  so  it  is  thought  that  the  fluid  caloric  goes 
into  and  fills  the  molecular  spaces. 

The  sun  and  stars  throw  off  abundance  of  this  sub- 
stance, and  shoot  it  with  the  velocity  of  light  across 
the  spaces  between  them  and  the  earth.  In  the  cases 
of  friction,  of  blows,  and  of  pressure,  the  molecules  of 
bodies  are  pushed  nearer  together,  and  by  this  means 
the  caloric  is  squeezed  out  from  between  them,  as,  wheii 


NATURAL    PHILOSOPHY.  225 

a  wet  sponge  is  pressed,  water  flows  from  its  interstices 
In  chemical  action  also,  the  particles  of  bodies  are 
brought  nearer  together  and  force  the  heat  fluid  from 
between  them.  This  theory,  which  until  lately  was 
opposed  by  only  a  few  eminent  men,  is  now  almost  uni- 
versally discarded. 

2.  The  dynamic  theory. — It  is  now  generally  be- 
lieved that  heat  is  a  kind  of  vibration.  This  theory, 
like  the  other,  supposes  matter  to  be  made  up  of  mole- 
cules separated  by  definite  distances ;  it  goes  further, 
and  supposes  these  molecules  to  be  in  motion,  rapidly 
vibrating  in  the  minute  spaces  between  them.  To  in- 
crease the  rapidity  of  this  motion  is  to  make  a  body 
hot ;  to  lessen  it  is  to  make  the  body  cold.  The  theory 
assumes  also  the  existence  of  the  ether,  which  according 
to  the  theory  of  light  must  fill  all  space. 

When  we  step  from  the  shade  into  the  sunlight,  the 
gentle  heat  of  its  rays  is  instantly  felt.  The  explana- 
tion is  this  :  the  molecules  of  the  sun  itself  are  in  rapid 
vibration,  they  impart  motion  to  the  ether,  whose  vibra- 
tions dart  through  the  space  between  the  sun  and  us,  and, 
coming  in  contact  with  the  person,  impart  vibration  to 
the  molecules  of  the  sense  of  touch,  when  we  become 
immediately  conscious  of  the  presence  of  heat. 

When  bodies  are  heated  by  friction,  their  molecules 
are  made  to  vibrate  faster  by  the  rubbing.  Heat  is 
evolved  by  percussion,  because  a  blow  increases  the 
motion  of  the  already  trembling  particles  of  the  body 
struck.  The  same  effect  is  produced  by  pressure. 

§  2.    OF   THE    TRANSMISSION    OF   HEAT. 

(81.)  Kays  of  heat,  like  rays  of  light,  pass  through 
10* 


226  NATURAL    PHILOSOPHY. 

some  bodies  more  freely  than  through  others.  They 
obey  the  same  laws  of  transmission,  of  reflection,  and 
of  refraction. 

1.  Rays  of  heat. — Since  heat   and  light   come   to- 
gether in  the  sunbeam,  and  since  they  are  thought  to 
be  of  the  same  nature,  both  being  the  result  of  vibra- 
tions, we  may  speak  of  rays  of  heat,  just  asjwe  do  of 
rays  of  light. 

2.  Transmission  of  heat  rays.  — Just  as  light  passes 
more  freely  through  some  bodies  than  through  others, 
so  heat  passes  through  different  bodies  with  different 
degrees  of  facility.     Those  bodies  through  which  it 
passes  most  freely,  are  said  to  be  diathermic,  while 
those  through  which  it  can  go  with  the  greatest  difficulty, 
are  said  to  be  athermic. 

Heat  from  different  sources  is  transmitted  in  dif- 
ferent degrees  through  the  same  substance.  It  is,  for 
example,  a  familiar  fact  that  the  glass  of  our  windows 
allows  the  heat  of  the  sun  to  enter  our  rooms,  while  it 
prevents  the  heat  of  the  stove  from  going  out. 

Rock-salt  is  the  most  diathermic  substance  known ; 
it  allows  heat  from  all  sources  to  pass  through  it  with 
the  greatest  freedom. 

3.  Laws   of   transmission. — Heat    passes    through 
space  with  the  same  remarkable  velocity  as  light.     It 
obeys  the  same  laws  of  transmission.   [See  (60).] 

4.  Law  of  reflection. — Heat  is  also  reflected  in  the 
Bame  way  that  light  is.     For  the  law  which  it  obeys, 
see  (61). 

In  former  times,  when  the  open  fireplace  was  com- 
mon, the  housewife  baked  her  bread  by  heat  reflected 
from  the  top  of  a  tin  oven  placed  before  the  fire.  This 
oven,  once  found  in  every  kitchen,  now  only  in  the  gar 


NATURAL    PHILOSOPHY.  227 

ret  if  found  at  all,  having  been  pushed  out  by  the 
modern  stove,  consisted  of  a  tin  box  closed  at  the  back 
and  the  ends,  open  in  front,  and  having  its  top  slanting 
at  an  angle  of  about  45°.  A  horizontal  shelf  was 
placed  in  the  middle  of  the  oven,  upon  which  stood  the 
loaf  to  be  baked.  Under  the  shelf  was  another  slant- 
ing tin  surface.  The  oven  standing  with  its  open  face 
to  the  blazing  fire,  received  the  heat  rajs  upon  its  two 
slanting  surfaces,  and  reflected  them  against  the  top 
and  bottom  of  the  loaf. 

5.  Law  of  refraction. — Heat  is  also  refracted  like 
light.  [See  (68).] 

The  sun's  heat  coming  through  the  window-glass  is 
bent  from  its  course.  By  a  double  convex  lens  it  may 
be  collected,  and  its  intensity  greatly  increased.  The 
common  burning  glass  illustrates  this.  It  may  be  a 
spectacle  glass  held  by  the  hand  in  a  sunbeam,  and 
the  small  bright  spot — the  focus  of  light — is  also  the 
focus  of  heat.  The  other  hand  held  at  this  point 
will  be  burned ;  tinder  will  be  set  on  fire,  or  gunpowder 
exploded. 

(f,2.)  Heat  tends  to  diffuse  itself  equally  among  all 
bo- lies.  This  distribution  takes  place  in  three  ways ; 
by  conduction,  by  convection,  and  by  radiation. 

1.  The  equal  diffusion  of  heat. — If  two  bodies,  one 
cold,  the  other  hot,  be  placed  near  each  other,  it  will  in 
a  short  time  be  found  that  both  are  equally  warm. 
The  cold  body  has  received  more  heat,  the  hot  body  has 
parte.'  with  some  that  it  had.  What  is  thus  true  of  two 
bodif/.  is  true  of  all.  Bodies  are  constantly  giving  and 
receiv  .ng  heat.  Those  which  part  with  more  than  they 
rece«'<  from  others,  get  colder;  those  which  receive 


228  NATURAL    PHILOSOPHY. 

more  than  they  give,  get  warmer.  Ice,  for  example,  is 
giving  heat  to  all  bodies  around  it ;  it  is  at  the  same 
time  receiving  heat  from  them  in  return.  Ice  will  ac- 
tually warm  a  body  which  is  colder  than  itself,  because 
it  will  give  more  heat  than  it  gets  in  return  ;  it  will  be 
melted  by  a  body  warmer  than  itself,  because  it  receives 
more  than  it  gives. 

i. — CONDUCTION. 

A". — Heat  is  conducted  through  some  bodies  much 
more  freely  than  through  others.  Among  solids  the 
metals  are  the  best  conductors.  Liquids  are  poor  con- 
ductors, and  gases  still  poorer. 

1.  Conduction. — Heat  is  transmitted  by  conduction 
when  it  goes  to  different  parts  of  the  same  body  by 
traveling  step  by  step  from  molecule  to  molecule. 

To  illustrate  this  definition,  suppose  that  one  end  of 
a  cold  iron  rod  is  held  in  the  flame  of  a  lamp.  The 
heat  will  travel  gradually  from  the  flame  through  the 
rod,  until  the  distant  end  gets  too  warm  to  be  held  by 
the  hand. 

Now,  if  we  would  understand  how  the  heat  has  made 
its  little  journey  through  the  rod,  we  must  picture  to 
ourselves  the  delicate  motion  of  the  molecules  of  the 
iron.  Those  molecules  in  contact  with  the  flame  are 
made  to  vibrate ;  they  swing  against  their  neighbors  and 
put  them  also  in  more  rapid  motion  ;  they,  in  turn,  give 
motion  to  the  ne'xt,  and  these  to  the  next,  until  those  at 
the  distant  end  of  the  rod  have  finally  received  the 
shock.  The  vibrations  of  these  molecules  of  the  rod, 
impart  motion  to  the  molecules  of  the  hand  in  contact 
with  them ;  the  delicate  Derves  of  touch  receive  the  im 


NATURAL    PHILOSOPHY.  229 

pulses,  and  announce  the  pain.     The  hand  is  burned; 
the  rod  is  hot. 

Some  bodies  conduct  heat  more  freely  than  othera 
Those  which  conduct  heat  freely  are  called  conductors : 
those  which  hinder  its  passage  much,  are  called  poor 
conductors,  and  those  which  nearly  or  quite  forbid  its 
passage,  are  called  non-conductors. 

2.  Metals  are  good  conductors. —  Among  solid  bodies 
the  metals,  as  a  class,  are   the  best   conductors,  but 
among  metals  there  is  great  difference  in  conducting 
power.     By  a  very  simple  experiment  this  may  be  il- 
lustrated.    Plunge  two  spoons,  one  of  silver  and  the 
other  of  German  silver,  into  the  same  cup  of  hot  tea ;  it 
will  be  found  that  the  upper  end  of  the  silver  spoon  will 
get  hot  much  quicker  than  that  of  the  other.     Among 
the  best  conductors  we  find  silver,  copper,  gold,  brass, 
tin,  and  iron,  in  the  order  named. 

3.  Conduction  in  liquids. — The  conducting  power  of 
liquids  is  very  feeble.     Water,  for  example,  may  be 
boiled  in  a  glass  tube,  with  ice  at  the  bottom  without 
melting  it,  by  applying  the  heat  to  the  top  of  the  water, 
or  near  the  upper  end  of  the  tube. 

4.  Conduction    of   gases. — Whether  gases   conduct 
heat  in  the  least  degree  is  doubted.     Dry  air  is  surely 
among  the  poorest  conductors,  and  so,  likewise,  are  all 
porous  substances  in  which  large  quantities  of  air  are 
inclosed. 

n. — CONVECTION. 

B. — Convection  takes  place  in  bodies  whose  particles 
are  free  to  move.  Air  is  heated  in  no  other  way. 
Liquids  are  also  heated  by  convection,  but  it  can  not 
occur  in  solids. 


230  NATURAL    PHILOSOPHY. 

1.  Convection. — Heat  is  transmitted  bj  convection 
when  it  is  carried  from  place  to  place  by  moving  parti- 
cles of  matter.     The  following  very  simple  experiment 
will  make  this  definition  clear.     Upon  a  plate  of  thick 
glass  or  a  smooth  block  of  wood  put  a  bit  of  candle, 
lighted,  and  over  it  place  a  lamp-chimney  so  that  its  edge 
may  project  a  little  beyond  the  edge  of  the  block  (Fig 
116.)     If  the  edge  of  the  chimney  fits  closely  upon  the 

FI  lie  top  of  the  block  so  that  no  air  can  enter, 
except  at  the  open  part  A,  the  flame  will 
flutter  violently,  showing  that  air  is  forc- 
ed against  it.  If  now,  some  light  sub- 
stance, such  as  down  or  cotton,  be  hung 
from  a  thread  above  the  top  of  the  chim- 
ney, it  will  be  lifted  away,  showing  that 
air  is  rising  out  of  the  chimney.  Now,  we  know  al- 
ready that  air  is  expanded  by  the  heat,  and  we  learn 
from  this  experiment  that  the  cold  air  going  under  the 
glass  pushes  the  expanded  air  away  from  the  flame,  up 
and  out  at  the  top  of  the  chimney.  This  motion  of 
heated  air  is  convection. 

"What  we  have  seen  in  this  experiment  really  takes 
place  whenever  a  hot  body  is  surrounded  by  colder  air. 
The  air  in  contact  with  a  hot  stove,  for  example,  is 
heated  and  expanded.  The  colder  air  then  pushes  it 
away  and  takes  its  place,  only  in  turn  to  be  heated  and 
pushed  away  by  other  colder  portions.  The  air  goes  to 
the  stove,  becomes  heated,  and  moves  away  to  other 
parts  of  the  room,  carrying  the  heat  with  it.  This 
transfer  of  heat  by  the  moving  particles  of  air  is  called 
convection. 

2.  Air  is  heated  in  nc  other  way. — Air  is  heated  only 
by  convection.    The  heat  of  a  stove  does  not  go  out  to 


NATURAL    PHILOSOPHY.  231 

distant  parts  of  a  room  to  warm  the  air :  the  air  must 
go  to  the  stove  to  get  warm.  So,  too,  the  atmosphere 
is  warmed  by  convection.  The  sunbeams  coming 
through  it  do  not  warm  it ;  they  only  warm  the  earth 
beneath  it.  Nor  does  the  heat  of  the  earth  pass  from 
particle  to  particle,  as  it  may  in  solid  bodies ;  the  heat 
of  the  earth  warms  only  those  particles  in  immediate 
contact  with  it.  These  rise  and  carry  their  heat  with 
them  to  upper  regions,  while  colder  ones  take  their 
places  in  contact  with  the  ground  to  get  warm  in  turn, 
and  then  ascend. 

3.  Liquids  heated  by  convection. — Liquids  are  also 
heated  by  convection*    A  simple  experiment  will  illus- 
trate the  convection  of  water.    Into  a  flask  or  bottle  of 
water  put  a  little   cochineal.      Its  particles  are  just 
about  as  heavy  as  those  of  the  water,  and  will  show  by 
their  motion  whether  there  are  currents  in  the  water. 
Warm  the  bottom  of  the  bottle,  and  the  heated  water 
will  be  seen  to  be  rapidly  leaving  the  bottom,  while 
other  portions  are  moving  downward  to  take  its  place. 

4.  No  convection  in  solids. — Solids  can  not  be  heated 
by  convection  simply  because  their  particles  are  not  free 
to  move  among  themselves. 

in. — RADIATION. 

C. — Heat  is  distributed  by  radiation  from  all  bodies. 
The  amount  of  heat  which  a  body  can  radiate  depends 
upon  its  temperature,  its  nature,  and  the  condition  of 
its  surface. 

1.  Radiation. — Heat  is  transmitted  by  radiation 
when  it  goes  in  straight  lines,  in  all  directions,  through 
non-conducting  media. 


232  NATURAL    PHILOSOPHY. 

The  air  is  a  non-conductor,  yet  heat  passes  through 
it  with  the  greatest  freedom.  Let  a  red  hot  iron  ball 
be  suddenly  placed  in  a  cold  room  ;  a  person  at  a  little 
distance  will  almost  instantly  feel  its  heat  rays  falling 
upon  his  face.  The  heat  is  not  brought  to  him  by  con 
vection,  because  he  feels  it  just  as  well  whether  the  ball 
is  above  his  face,  below  it,  or  beside  it,  while  the  heated 
air  can  move  only  upward.  It  is  transmitted  by  radia- 
tion. The  heat  of  the  sun  comes  to  us  through  space 
where  there  is  no  solid  body  to  conduct  it,  no  liquid  nor 
gaseous  substance  to  bring  it  to  us  by  convection.  It 
is  radiated  to  us. 

It  is  chiefly  by  radiation  that  the  general  distribu- 
tion of  heat  is  accomplished.  All  bodies,  at  all  tem- 
peratures, are  radiating  heat.  That  which  radiates 
more  than  it  receives  from  others,  grows  cold,  while  that 
which  gives  less  than  it  gets,  grows  warm. 

2.  Depends  on  temperature,  nature,  condition. — The 
higher  the  temperature  of  a  body,  the  more  heat  it  can 
radiate.  Moreover,  bodies  of  different  substance,  when 
at  the  same  temperature,  give  off  different  quantities 
of  heat  in  the  same  time.  Thus,  iron  is  a  better  radia- 
tor than  gold.  Still  farther,  the  same  body,  at  the  same 
temperature,  with  a  rough  surface  will  radiate  much 
faster  than  when  its  surface  is  smooth.  The  rough 
surface  of  a  cast  iron  stove,  for  example,  is  a  better  ra 
diator  than  if  it  were  polished. 

§   3.   ON  THE   EFFECTS   OF   HEAT. 

(83.)  The  action  of  heat  is  twofold ;  it  raises  the 
temperature  of  a  body  to  which  it  is  applied,  and  at  the 
Bame  time  expands  it.  This  is  true  of  its  action  upon 
solid,  liquid,  and  gaseous  bodies. 


NATURAL    PHILOSOPHY.  233 

Temperature  is  measured  by  the  expansion  which 
accompanies  it,  in  instruments  called  thermometers. 
There  are  three  varieties  of  thermometers  in  use,  the 
Fahrenheit,  the  Centigrade  and  the  Reaumer.  The 
air  thermometer  is  used  to  show  delicate  changes  of 
temperature. 

1.  The  action  of  heat  is  twofold. — That  the  temper- 
ature of  bodies  is  raised  by  the  application  of  heat  is  too 
familiar   to   need  illustration.     That   while   the  tem- 
perature rises,  the  body  grows  larger,  is  known  by  such 
facts  as  the  following : — A  ball  of  metal,  which,  when 
cold,  just  fits  a  ring,  will  be  too  large  to  enter  it  when 
hot.     A  clock  pendulum  is  longer  in  summer  than  in 
winter.     The  tire  of  a  carriage  wheel  is  put  on  while 
hot ;  on  cooling,  it  contracts  and  binds  the  parts  of  the 
wheel  firmly  together. 

2.  The  expansion  of  solids. — To  show  the  expansion 
of  a  metallic  bar,  the  following  beautiful  experiment  has 
been  devised.     A  rod  of  metal  (R,  Fig.  117),  is  fixed 
at  one   end   E,  while   the  other  end,  passing   freely 
through  a  post,  presses  against  a  bar  of  brass  B.     One 
end  of  this  bar  is  fastened  by  a  hinge  A,  while  upon 
the  other  end  above,  rests  another  bar  ~D.     This  second 
bar  also  turns  upon  a  hinge,  and  upon  its  other  end,  it 
carries  a  small  plain  mirror  M. 

If  a  beam  of  sunlight  S,  coming  through  a  hole  in 
the  shutter  of  a  partially  darkened  room,  is  made  to 
fall  upon  the  mirror,  it  will  be  reflected,  and  form  a 
white  spot  upon  a  distant  wall  or  ceiling.  This  spot 
will  be  quite  still  as  long  as  the  mirror  does  not  move, 
but  when  the  mirror  rises,  the  spot  will  move  along  the 
ceilirg  rapidly.  Now,  let  the  rod  R,  be  heated,  and 


234 


NATU  RAL    PHILOSOPHY. 


the  spot  moves.  The  rod  must  be  expanded,  so  as  to 
push  against  the  first  bar  B,  the  upper  end  of  which 
pushes  against  the  second  bar  D,  and  lifts  the  mirror. 


Fig.  11T. 


If  the  air  in  the  room  is  dusty,  .the  entire  beam  of  re- 
flected light  L,  can  be  seen,  tracing  a  luminous  path 
upon  the  ceiling,  while  the  bar  expands. 

Different  solids  expand  unequally  for  the  same  in- 
crease of  temperature,  but  each  solid  expands  uniformly, 
— that  is  to  say,  two,  three,  or  ten  degrees  of  heat  will 
produce  respectively  two,  three,  or  ten  times  as  much 
expansion  as  one  degree. 

3.  The  expansion  of  liquids. — The  expansion  of  a 
liquid  by  heat,  may  be  shown  by  filling  a  bottle  with 
water,  and  then,  after  fitting  into  the  cork  a  glass  tube 
open  at  both  ends,  and  tightly  pressing  the  cork  into 
the  neck,  standing  it  in  a  vessel  of  warm  water.  The 
water  in  the  bottle  will  be  heated,  and  its  expansion 


NATURAL    PHILOSOPHY.  $35 

will  be  shown  by  the  fluid  rising  higher  and  higher  in 
the  tube. 

A  little  artifice  enables  one  to  change  this  slow  mo- 
tion into  another  so  rapid,  that  it  may  be  easily  seen 
even  by  those  in  the  most  distant  part  of  the  room.  A 
very  long  slender  body,  a  rye  straw  full  length  answers 
the  purpose  admirably,  is  suspended  by  a  thread  tied 
near  to  one  end.  From  this  end  (E,  Fig.  118),  is  hung 

Fig.  lia 


a  little  cylinder  of  metal,  of  such  weight  as  to  be  almost 
balanced  by  the  long  arm  of  the  straw  lever.  The 
cylinder  hangs  inside  of  the  tube  of  the  bottle,  and 
rests  upon  the  water  in  it.  Now,  when  the  water  in 
the  bottle  expands,  it  rises  in  the  tube,  and  pushes  the 
little  cylinder  up  before  it.  "While  it  goes  up,  the  other 
end  of  the  straw  lever  goes  down  many  times  faster. 
The  rapid  sinking  of  the  straw,  while  the  water  is  being 
heated,  shows  that  the  water  is  expanding. 

All  liquids  are  expanded  by  heat,  but  some  are  much 
more  affected  than  others.  The  expansion  of  liquids  is 
much  less  uniform  than  that  of  solids. 

4.  The  expansion  of  gases. — All  gases  are  expanded 


236  NATURAL    PHILOSOPHY. 

by  heat.     For  illustration  by  experiment,  of  the  ex- 
pansion of  air  read  (16.)  2. 

The  expansion  of  gases  is  more  nearly  uniform 
than  that  of  either  solids  or  liquids,  and  much  greater 
for  the  same  addition  of  heat.  What  is  more  remark- 
able is  the  fact  that  they  all  expand  at  the  same  rate. 
If  we  have  490  cubic  inches  of  air  at  a  temperature  of 
32°  F.  and  add  one  degree  of  heat,  there  will  be  491 
cubic  inches:  it  expands  -^  of  its  bulk.  All  gases 
expand  at  the  same  rate,  ^  of  their  bulk,  at  32°  for 
every  additional  degree.  This  fraction  (^-J^j-)  is  called 
the  coefficient  of  expansion  for  gases. 

5.  Temperature  measured  ~by  expansion. — We  have 
found  that  temperature  and  expansion  increase  at  the 
same  time  by  the  addition  of  heat.     Moreover,  in  the 
same  body  a  certain  amount  of  expansion  always  occurs 
with  the  same  increase  of  temperature.     By  seeing  the 
expansion  we  may  therefore  judge  of  the  increase  of 
temperature. 

The  expansion  of  solids  is  too  slight,  while  that  of 
gases  is  too  great,  to  be  conveniently  used  to  measure 
the  changing  temperature  of  the  air  and  other  things. 
Mercury  is  a  liquid  metal,  whose  expansion  is  remark- 
ably uniform,  and  neither  too  great'  nor  too  little  for 
practical  purposes.  All  common  thermometers  are 
made  with  it. 

6.  The  thermometer. — The    mercurial  thermometer 
consists  of  a  glass  tube  terminating  at  one  end  in  a 
bulb,  and  sealed  at  the  other.     The  bulb  and  lower 
part  of  the  tube  are  filled  with  mercury,  the  space  in 
the  tube  above  the  mercury  being  a  vacuum.     Behind 
the  tube  is  a  graduated  scale  to  show  the  height  of  the 
column  of  mercury. 


NATURAL    PHILOSOPHY.  237 

7.  Various  forms. — There  are  three  modes  of  gradu- 
ating the  scale,  and  this  gives  rise  to  three  varieties  of 
mercurial  thermometer.     In  Fahrenheit 's  instrument, 
the  zero  of  the  scale  marks  the  height  of  the  mercury 
in  the  tube  when  the  bulb  is  placed  in  a  mixture  of 
gnow  and  salt.  When  the  bulb  is  put  into  boiling  water, 
the  mercury  in  the  tuba  runs  up  to  a  point  which  is 
marked  212  on  the  scale.     The  distance  between  these 
points  is  divided  into  212  equal  parts  called  degrees, 
and  this  graduation  is  carried  above  and  below  these 
points.     According  to  this  thermometer,  water  boils  at 
212°  and  freezes  at  32°. 

In  the  centigrade  thermometer,  the  zero  point  marks 
the  height  of  the  mercury  in  the  tube  when  the  bulb  is 
placed  in  freezing  water.  The  height  to  which  it  rises 
when  the  bulb  is  put  into  boiling  water,  is  marked  100, 
and  the  distance  between  these  points  is  divided  into 
100  equal  parts.  The  boiling  point  of  water  is,  there- 
fore, 100°  ;  its  freezing  point  is  0°. 

In  Reaumer's  thermometer,  the  zero  marks  the  freez- 
ing point  of  water ;  the  boiling  point  is  called  80. 

Degrees  of  temperature  below  the  zero  points  ai'e 
generally  indicated  by  the  minus  sign  (— )  placed  be- 
fore jthe  number.  Thus,  —  40°,  means  a  temperature 
40°  below  zero. 

8.  Other  forms. — Mercury  freezes  at  about  —  39° . 
temperatures  below  this  point  are  measured  by  ther- 
mometers containing  alcohol.    Mercury  boils  at  660°  : 
temperatures  above  this  point   are  measured  by  the 
expansi  )n  of  solid  bodies. 

When  it  is  necessary  to  show  very  delicate  changes 
of  temperature,  the  air  thermometer  is  used.  This  in- 
strument has  a  variety  of  forms,  but  it  consists  essen- 


NATURAL    PHILOSOPHY. 

tially  of  a  glass  tube,  terminating  at  one  end  in  a  bulb, 
the  other  end  being  open  and  inserted  into  a  cistern 
Fig.  U9.  of  colored  liquid.  (See  Fig.  119.)  The  liquid 
fills  a  part  of  the  tube ;  the  rest  of  the  tube 
and  the  bulb  above  is  filled  with  air.  A  grad- 
uated scale  is  placed  behind  the  tube.  The 
air  expands  or  contracts  with  every  change 
of  temperature,  and  accordingly  drives  the 
colored  liquid  down,  or  allows  it  to  rise 
in  the  tube.  The  motion  of  the  liquid  shows 
the  change  in  the  temperature. 

(84.)  Temperature  indicates  the  rapidity 
of  vibration  of  the  molecules  of  bodies: 
expansion  indicates  a  change  in  their  rela- 
tive positions.  The  heat  which  produces  the 
first  is  called  sensible  heat :  that  which  pro- 
duces the  second  is  called  latent  heat.  The 
sum  of  both  quantities  in  any  body,  com- 
pared to  the  sum  of  both  in  some  other 
body  taken  as  a  standard,  is  called  the 
specific  heat. 

1.  Rapidity  of  motion  and  change  of  position. — He 
who  has  a  clear  idea  of  the  molecules  [see  (4.)  1],  can 
distinctly  imagine  the  multitude  of  these  little  bodies 
of  which  any  larger  body  is  made  up,  separated  from 
each  other  by  minute  distances  and  in  rapid  motion. 
Now,  heat  can  make  them  vibrate  faster :  it  may  also 
push  them  farther  apart,  or  otherwise  change  their  posi- 
tion ;  it  can  do  nothing  more.  Then,  when  heat  is 
being  applied  to  a  bar  of  iron,  let  the  mind  picture  to 
itself  these  two  effects ;  the  molecules  of  the  bar  vibrat- 
ing more  and  more  swiftly,  and  at  the  same  time  being 


NATURAL    PHILOSOPHY.  239 

pushed  farther  and  farther  apart.  Tlie  first  of  these 
effects  is  manifested  as  temperature,  the  second  as 
expansion. 

2.  Sensible  and  latent  heat. — The  heat  which  is  ex- 
pended in  raising  temperature  is  called  sensible  heat ; 
it  can  affect  the  sense  of  touch.     That  which  is  used  to 
produce  expansion,  is  called  latent  heat;  it  does  not  af- 
fect the  sense  of  touch.     Now,  the  heat  that  goes  into, 
or  acts  upon,  any  body,  is  divided  into  these  two  por- 
tions; one  part  sensible,  the  other  latent. 

3.  Specific  heat. — But  different  substances   do  not 
divide  it  alike ;  that  is,  if  the  same  amount  be  added  to 
two  substances,  one  of  them  will  devote  more  of  it  to 
temperature  and  less  to  expansion,  than  the  other. 

Let  equal  weights  of  water  and  mercury  be  placed 
over  the  same  source  of  heat.  The  water  divides  the 
heat  it  receives  into  two  parts,  one  to  raise  its  tempera- 
ture, the  other  to  expand  it.  The  mercury,  receiving 
the  same  amount,  divides  it  into  two  parts  devoted  to 
the  same  purposes,  but  the  heat  devoted  to  temperature 
is  more  than  in  water,  while  that  devoted  to  expansion 
is  less.  We  find  that  the  temDerature  of  mercury  rises 
much  faster  than  that  of  water  :  it  takes  thirty  times  as 
long  to  raise  the  water  to  a  given  temperature  as  it 
does  the  mercury.  If  it  take  thirty  times  as  long, 
and  one  receives  heat  as  fast  as  the  other,  there  must 
be  thirty  times  as  much  heat  in  the  water  as  in  the 
mercury  when  that  temperature  is  reached  by  both. 
We  see,  then,  that  at  the  same  temperature  different 
substances  may  have  very  different  quantities  of  heat 
in  them.  The  relative  quantities  of  heat  in  different 
bodies  at  the  same  temperature  is  called  specific  heats. 
Water  is  the  standard  of  st>ecific  heat.  At  a  given 


240  NATURAL    PHILOSOPHY. 

temperature  it  contains  more  heat  than  any  othei 
known  substance.  Its  specific- heat  being  1,  the  specific 
heats  of  all  other  substances  are  fractional.  The  spe- 
cific heat  of  mercury  is  .03.  By  this  is  meant,  that 
when  equal  weights  of  mercury  and  water  are  at  the 
Bame  temperature,  the  mercury  will  contain  only  .03  as 
much  heat  as  the  water. 

(85.)  The  expansion  of  a  solid  body  will  continue 
nearly  uniform  until  its  temperature  has  reached  the 
melting  point.  The  temperature  then  stops  rising, 
while  the  expansion  increases  and  continues  until  the 
solid  is  melted. 

1.  The  melting  point. — The  temperature  at  which  a 
solid  body  begins  to  melt,  is  called  its  melting  point. 
At  this  point,  the  repulsive  force  of  heat  nearly  balances 
the  cohesion  of  the  molecules,  and  enables  them  to  move 
freely  among  themselves.     The  body  becomes  a  liquid, 
and  the  change  is  called  liquefaction.     The  melting 
point  for  different  substances  is  not  the  same.     Ice 
melts  at  32°  F.;  mercury  at  .—39°;  iron  at  about  3,000° 
and  platinum  at  about  5,000°. 

2.  The  temperature  stops  rising. — If  heat  be  applied 
to  a  vessel  of  ice  at  32°,  the  ice  will  melt  and  the  water 
formed  will  have  the  same  temperature,  323.     So,,  too. 
when  wax,  or  iron,  or  lead  is  melted,  the  liquid  will 
have  the  same   temperature   as    the   solid   which   is 
melting. 

3.  But  the  expansion  increases. — But  in  the  case  of 
all  the  substances  above  named,  except  ice,  the  ex- 
pansion is  greater  at  the  melting  point  than  before  it 
was  reached.     The  liquid  fills  more  space  than  the 
solid  from  which  it  was   formed.      It  should   be  so. 


NATURAL    PHILOSOPHY.  241 

because  the  heat  force  is  all  expended  to  change  the 
position  of  the  molecules,  whereas,  before,  a  part  of  il 
was  used  up  to  produce  a  rise  of  temperature. 

Ice  contracts  when  melting ;  the  water  formed  fills 
.ess  space  fhan  the  ice.  In  this  case,  likewise,  all  the 
heat  applied  is  expended  in  changing  the  position  of 
the  molecules,  but  not  in  pushing  them  farther  apart, 
for  they  occupy  less  space  than  before  the  change  oc- 
curred. The  change  consists  in  throwing  the  molecules 
out  of  their  crystalline  arrangement.  The  water  will 
continue  to  contract  until  it  reaches  a  temperature  of 
39°,  after  which  it  expands. 

Those  who  have  attempted  to  melt  ice  or  snow,  for 
domestic  purposes,  remember  how  slow  the  process  is. 
The  amount  of  heat  required  to  simply  melt  the  snow 
without  making  it  any  warmer,  is  very  great ;  the  same 
amount  applied  to  the  water  formed,  would  raise  its 
temperature  142°.  Hence  the  latent  heat  of  water  is 
said  to  be  142°. 

(86.)  The  expansion  of  a  liquid  will  continue  grad- 
ual until  the  boiling  point  is  reached,  a  temperature 
depending  upon  the  purity  of  the  liquid,  upon  the 
nature  of  the  vessel  in  which  it  is  heated,  and  upon  the 
pressure  it  sustains.  At  the  boiling  point,  the  temper- 
ature stops  rising,  while  the  expansion  greatly  increases, 
and  continues  until  the  liquid  is  vaporized. 

1.  The  boiling  point. — The  temperature  at  which  a 
liquid  begins  to  boil,  is  called  its  boiling  point.  At 
this  temperature,  the  repulsive  force  of  heat  entirely 
overcomes  the  cohesion  of  the  molecules,  and  drives 
them  just  as  far  apart  as  possible.  The  body  rapidly 
becomes  a  vapor,  and  the  change  is  called  vaporization. 
11 


242  NATURAL    PHILOSOPHY, 

Liquids  do  indeed  change  to  vapor  at  all  temperatures. 
Even  from  freezing  water,  more  or  less  vapor  is  ever 
slowly  rising.  This  slow  change  is  called  evaporation. 
The  boiling  point  for  different  liquids  is  not  the  same. 
Water  boils  at  212°,  Alcohol  at  173°,  Ether  at  95°. 
The  boiling  point  for  the  same  liquid  is  not  the  same  ; 
it  depends  upon  three  circumstances. 

2.  It  depends  on  the  purity  of  the  liquid. — It  is  af- 
fected,  first,   by   the  presence  of  impurities    in    the 
liquid.     The   presence   of  some  impurities  raises  the 
boiling  point ;  of  others,  lowers  it.     Salt  water,  for  ex- 
ample, boils  at  a  higher  temperature  than  pure  water, 
while  that  which  contains  air,  boils  at  a  much  lower 
temperature  than  that  which  contains  none. 

3.  It  depends  on  the  nature  of  the  vessel. — In  an  iron 
vessel,  water  will  boil  at  a  lower  temperature  than  in 
one  of  glass.     It  is  so  because  there  is  a  stronger  adhe- 
sion between  water  and  glass,  than  between  water  and 
iron.     The  stronger  adhesion  requires  a  stronger  heat 
to  overcome  it. 

4.  It  depends  on  the  pressure. — But  the  most  import- 
ant circumstance  on  which  the  boiling  point  of  a  liquid 
depends,  is  the  pressure  it  sustains.     This  pressure  is 
due  to  the  atmosphere,  to  the  weight  of  the  liquid  it- 
self, and  to  any  force  which  may  be  brought  to  bear 
upon   it  by   artificial  means.     Whatever   may  be  its 
cause,  the  effect  of  pressure  is  to   raise   the  boiling 
point.     It  is  well  known  that  water  boils  at  a  lowei 
temperature  on  the  top  of  a  mountain  than  at  its  base 
It  does  so  because  the  pressure  of  the  air  upon  it  is 


This  very  important  principle  may  be  easily  illus- 
trate! by  experiment.     For  this  purpose  take  a  glass 


NATURAL    PHILOSOPHY.  243 

flask,  or  better,  a  bolt  head  (Fig.  120),  and  put  into  it 
water  enough  to  fill  the  stem  and  a  small  part  of  the 
bulb.  Invert  it  so  that  the  water  may  be  boiled  by 
holding  the  bulb  over  the  flame  of  a  lamp.  Fig.  120. 
Boil  it  until  the  steam  issues  freely  from  the 
stem,  and  then,  removing  it  from  the  flame, 
cork  the  stem  at  the  same  instant.  The  air 
lias  been  driven  out  from  the  instrument,  and 
nothing  remains,  to  press  upon  the  water,  but 
steam.  Turn  the  bulb  upward  so  that  the 
water  may  fill  the  stem  ;  pour  cold  water  upon 
the  bulb,  and  the  water  inside  will  boil  vio- 
lently. Even  when  the  tube  has  become  so 
cold  that  it  may  be  handled  without  incon- 
venience a  fresh  bath  of  cold  water  will 
cause  the  boiling  to  continue.  It  boils  at 
the  low  temperature  because  the  cold  water, 
condensing  the  steam,  removes  the  pressure  from  its 
surface. 

5.  The  temperature  stops  rising. — ~No  matter  how 
much  heat  may  be  applied  to  boiling  water,  its  tem- 
perature can  not  be  raised.  Moreover,  the  temperature 
of  the  steam  is  always  that  of  the  water  from  which  it 
is  made. 

By  the  following  experiment  these  facts  may  be 
illustrated.  Water  is  placed  in  an  open  vessel  Y  (Fig. 
121).  Into  the  water  is  plunged  the  bulb  of  an  air 
thermometer  T,  whose  tube  is  bent  twice  at  right  an- 
gles for  the  purpose.  While  the  water  is  being  heated 
by  a  lamp-flame,  the  gradual  sinking  of  the  fluid  in  the 
stem  of  the  thermometer  shows  the  increase  of  tem- 
perature ;  but  when  the  water  fairly  boils,  the  fluid  stops 
sinking,  showing  that  the  temperature  no  longer  rises 


244 


NATURAL     PHILOSOPHY 


Fig.  121. 


The  fluid  will  remain  motionless  until  the  water  in  the 
vessel  has  been  changed  to  steam.  Let  the  bulb  be  lifted 
into  the  steam  above  the  water; 
no  change  occurs  in  the  height  of 
the  fluid  in  the  stem,  hence  the 
temperature  of  the  steam  must  be 
the  same  as  that  of  the  water. 

6.  But  the  expansion  increases* 
— If  all  the  heat  applied  to  a  boil- 
ing liquid  is  expended  to  produce 
expansion,  we  may  expect  that 
this  effect  will  be  more  rapid 
than  when  a  part  of  it  was  used 
to  raise  the  temperature.  This 
inference  is  abundantly  verified. 
.  Steam  fills  about  1  TOO  times  as 
much  space  as  the  water  from 
which  it  was  formed. 

The  amount  of  heat  required  to  expand  water  into 
,  in  other  words,  the  latent  heat  of  steam,  is  very 
great.  By  accurate  experiment  it  has  been  found  to 
be  972°  F.  The  steam  and  the  water  are  of  the  same 
tempeidture,  yet  there  is  an  excess  of  heat-force  in  an 
ounce  of  steam  which,  if  applied  to  one  ounce  of  water, 
would  be  sufficient,  were  it  possible,  to  raise  its  tem- 
perature to  972 ;  it  will  raise  the  temperature  of  nine 
ounces  of  water  108. 

(87.)  The  heat-force  which  has  been  required  to 
produce  expansion,  will  be  reproduced  when  the  ex- 
panded body  again  contracts. 

1.  Heat  restored  after  ~being  used. — The  following 
experiment  very  satisfactorily  shows  that  heat  is  re- 


NATURAL    PHILOSOPHY.  245 

quired  to  produce  expansion,  and  that  it  is  again  given 
off  when  contraction  occurs.  The  bulb  of  an  air  ther- 
mometer is  placed  in  a  receiver  over  the  plate  of  an 
air-pump ;  the  stem,  passing  through  the  top  of  the 
receiver,  is  bent  twice  at  right  angles,  and  is  filled 
with  its  colored  fluid  to  a  height  very  carefully 
marked.  By  a  few  rapid  strokes  of  the  piston,  the  air 
is  partly  exhausted  from  the  receiver ;  that  which  re 
mains  expands,  and  the  rising  of  the  fluid  in  the  ther 
mometer  shows  that  the  bulb  is  at  the  same  time 
cooled.  If,  now,  air  be  allowed  to  return  to  the  receiver, 
the  air  inside  becomes  more  dense,  and  the  sinking  of 
the  fluid  in  the  thermometer  shows  that  heat  is  again 
given  off. 

Numerous  familiar  facts  illustrate  this  principle. 
If  water  evaporates  from  the  hand,  it  cools  the  hand, 
because  the  hand  furnishes  the  heat  to  expand  the 
water  into  steam;  and  when  vapor  condenses  upon 
the  hand,  the  hand  is  warmed,  because  the  vapor  gives 
to  it  all  the  heat  which  had  been  used  to  keep  the 
water  in  the  form  of  steam. 

Bodies  in  contact  with  melting  snow  or  ice,  are 
cooled,  because  they  must  furnish  heat  to  change  the 
solid  to  the  liquid  form.  But  bodies  near  to  freezing 
water  are  warmed,  because  the  water  then  gives  up  the 
heat  which  had  been  needed  to  keep  it  in  a  fluid  form. 

§  4.   ON  THE   STEAM-ENGINE. 

(88.)  The  elastic  force  of  steam  is  applied  to  mechan- 
ical purposes  by  means  of  a  steam-engine.  The  essen- 
tial parts  of  this  machine  are,  1st,  the  boiler  in  which 
Bteam  is  generated;  2d,  the  cylinder  in  which  the 


246 


NATURAL    PHILOSOPHY. 


Fig.  122. 


steam  is  made  to  move  a  piston ;  3d,  the  crank  by 
whicli  the  piston  turns  a  wheel.  Engines  are  either 
high-pressure  or  low-pressure. 

1.  The  elastic  force  of  steam. — When  steam  is 
formed  at  a  temperature  of  212°,  its  elastic  force  is  juat 
equal  to  the  pressure  of  the  atmosphere,  or  151bs.  to 
the  square  inch.  If  taken  out  into  another  vessel,  pie- 
sen  ing  its  temperature  and  density,  it  would  exert  & 
pressure  of  151bs.  to  the  inch.  By  subjecting  water  ko 
a  greater  pressure,  its  boiling  point  is  raised,  and  the 
elastic  force  of  the  steam  will  be  increased.  The  Mar- 
cet's  globe  illustrates  this  principle.  It  consists  of  a 
metallic  globe  (Fig.  122),  which  is  furnished  with  a  long 
glass  tube  and  scale  T,  a  stop-cock  S, 
and  a  thermometer  A,  whose  bulb  is 
inside  the  globe.  In  the  bottom  of  the 
globe  is  a  little  mercury,  into  which  the 
end  of  the  tube  T  dips,  and  above  the 
mercury  is  a  quantity  of  water.  The 
water  is  boiled  until  the  air  is  driven 
out  of  the  open  stop  cock.  At  this  mo- 
ment, the  elastic  force  of  the  steam  is 
just  15  Ibs.  to  the  inch.  The  stop-cock 
is  now  closed :  the  thermometer  at  once 
shows  a  rise  of  temperature,  and  at  the 
same  time  the  mercury  begins  to  rise  in 
the  tube,  showing  an  increase  in  the 
force  of  the  steam.  When  the  temper- 
ature of  the  boiling  water  has  reached 
249 .5°,  the  expansive  force  of  the  steam 
w  is  equal  to  two  atmospheres,  or  301b». 

to  the  inch,  and  at  306°  it  is  five  atmospheres,  or  75 
Ibs.  to  the  inch. 


NATURAL     PHILOSOPHY. 


247 


Fig.  123. 


If,  now,  this  elastic  force  of  steam  can  be  made  to 
act  alternately  upon  opposite  sides  of  a  piston,  it  wil* 
knock  it  back  and  forth,  from  one  end  of  a  cylinder  to 
the  other  with  power  enough  to  move  any  amount  of 
other  machinery.  This  is  accomplished  in  the  steam- 
engine. 

2.  The  boiler. — The  boiler  of  a    steam-engine    is 
usually  made  of  plates  of  wrought-iron  riveted  togeth- 
er in  the  form  of  a  cylinder.     In  the  best  forms,  there 
are  tubes  which  run  lengthwise  through  the  body  of 
the  boiler,  through  which  the  flame  and  hot  gases  from 
the  fire  may  pass.     The  water  in  the  boiler  surrounds 
these  tubes,  and  is  rapidly  heated  by  them.   The  steam 
thus  formed  in  the  boiler  collects  above  the  water,  and 
by  its  pressure  raises  the  boiling  point  until,  when  its 
elastic     force    is    sufficiently 

great,  the  steam  is  allowed  to 
pass  through  a  pipe  to  the 
cylinder. 

3.  The  cylinder. — The  ar- 
rangement of  the  cylinder  and 
piston  are  shown  in  Fig.  123. 
The  pipe   which  brings    the 
steam   from  the  boiler  enters 
a   box    d,    from  which    two 
tubes  lead,  "one  to  the  top,  the 
other  to  the  bottom  of  the  me- 
tallic cylinder  C,  in  which  the 
piston    P,  moves.      Another 
tube  leads  from  this  box  out 
into  the  air,  or   away  to  an- 
other vessel,  where  the  steam, 
after  having  moved  the  piston, 


NATURAL    PHILOSOPHY. 

may  be  <!  ondensed.  A  sliding  valve,  Y,  is  so  arranged 
in  the  box  as  to  always  close  one  of  the  pipes  leading 
to  the  cylinder  and  leave  the  other  open.  If  the  upper 
tube  is  open,  as  represented  in  the  figure,  the  steam 
will  enter  above  the  piston  and  push  it  to  the  bottom  of 
the  cylinder  ;  if  the  lower  tube  is  open,  the  steam  'A  ill 
enter  below  the  piston  and  push  it  to  the  top.  In  either 
case  the  steam  -on  the  opposite  side  of  the  piston  will  be 
pushed  out  of  the  cylinder,  through  the  other  tube  and 
the  pipe,  O,  leading  from  the  cavity  under  the  sliding 
valve.  When  the  steam,  entering  through  the  lower 
tube,  has  pushed  the  piston  to  the  top  of  the  cylinder, 
the  valve  is  pushed  down  to  cover  the  end  of  that  tube, 
leaving  the  end  of  the  other  uncovered,  so  that  the 
steam  may  pass  through  it  to  act  above  the  piston.  By 
this  means  the  piston  will  be  alternately  pushed -back 
and  forth  from  one  end  of  the  cylinder  to  the  other. 

4.  The   crank. — By  this  simple  motion,  back  and 
forth,  the  piston  turns  a  wheel  by  means  of  a  crank. 
To  the  piston-rod,  A  (Fig.  123),  another  rod  is  joined 
by  a  hinge ;  the  other  end  of  this  rod  turns  a  wheel, 
from  which  motion  may  be  communicated  to  others  by 
bands  or  cogs. 

Besides  these  three  important  parts  of  the  steam 
engine,  there  are  numerous  other  appendages  for  par- 
ticular purposes,  such  as  a  safety-valve  attached  to  the 
boiler  to  regulate  the  pressure  of  steam  in  it ;  the 
governor  to  regulate  the  supply  of  steam  to  the  cylin- 
der ;  the  fly-wheel,  a  heavy  wheel  whose  inertia  causes 
the  motion  of  the  machine^  to  be  steady.  (See 
Silliman's  Physics.) 

5.  High  and  low  pressure  engines. — The  different 
forms  of  steam-engines  are  almost  as  numerous  as  the 


NATURAL    PHILOSOPHY.  249 

machinists  who  make  them,  or  as  the  variety  of  pur- 
poses to  which  they  are  applied.  There  are,  however, 
two  general  classes,  the  high-pressure  and  the  low-press* 
ure  engines. 

In  the  high-pressure  engines  the  steam,  after  moving 
the  piston,  is  thrown  out  from  the  cylinder  into  the 
air.  In  the  low-pressure  engines,  the  steam,  after 
moving  the  piston,  is  taken  off  to  a  vessel  called  the 
condenser,  in  which  it  is  changed  into  water.  The  first 
is  called  high  pressure,  because  the  steam  which  moves 
the  piston  must  push  the  steam  from  before  the  piston 
out  into  the  air,  which  presses  it  back  with  a  force  of 
15  Ibs.  to  the  inch.  To  do  this  evidently  requires  a 
pressure  of  15  Ibs.  to  the  inch  higher  than  in  the  other 
class,  in  which  the  steam  escapes  into  a  vacuum,  and 
of  course  exerts  no  pressure  against  the  piston. 
11* 


250  NATURAL    PHILOSOPHY. 


OHAPTEK    VIII. 


ON  ELECTRICITY. 

INTE  EDUCTION. — APPLICATION   OF    THE    FUNDAMENTAL 
IDEAS. 

(89.)  KEAD  (4).  A  constant  and  opposite  action  of 
attraction  and  repulsion  among  the  molecules  of  bodies 
gives  rise  to  the  phenomena  of  electricity. 

Of  the  nature  of  electricity  very  little  is  definitely 
known  ;  but  since  the  kindred  phenomena  of  light  and 
heat  have  been  found  to  be  the  result  of  vibratory 
motions  among  the  molecules  of  bodies,  the  tendency 
is  to  regard  electricity  also  as  the  effect  of  molecular 
vibrations  of  some  kind.  But  whether  we  adopt  this 
view,  or  still  cling  to  the  old  theory,  which  regards 
electricity  as  a  weightless  fluid  in  the  pores  of  all  bodies, 
we  may  describe  it  truly  as  a  manifestation  of  attrac- 
tion and  repulsion  acting  upon  the  molecules  of  a  body, 
thus  producing  an  effect  upon  the  body  itself. 

§  1.    OF  FEICTIONAL   ELECTRICITY. 

(90.)  Electricity  may  be  produced  by  friction.  The 
electrical  machine  is  an  apparatus  for  this  purpose.  It 
may  be  detected  by  instruments  called  electroscopes, 
showing  its  action  as  two  opposite  forces — attraction 
and  repulsion.  Its  intensity  may  be  measured  by  in- 


NATURAL    PHILOSOPHY.  251 

struments  called  electrometers.  It  is  governed  by  two 
laws : — 

1st.  Electricities  of  the  same  kind  repel  each  other ; 
of  different  kinds  attract. 

2d.  The  force  of  the  attraction  or  repulsion  is  in- 
versely as  the  square  of  the  distance  between  them. 

1.  Electricity  produced  by  friction. — If  a  well-dried 
glass  tube — a  lamp-chimney  for  example — be  thoroughly 
rubbed  with  a  flannel  cloth,  it  will  be  found  to  have 
new  and  curious  properties.     Hold  it  near  the  face, 
and  a  feeling  will  be  experienced  as  if  a  gentle  breeze 
were  blowing  against  the  cheek :  bring  it  nearer,  and 
perhaps  a  prickling  sensation  will  be  felt,  and  it  may 
be  that  a  crackling  sound  will,  at  the  same  time,  be 
heard;  or  approach  it  toward  some  very  light  sub- 
stances, such  as  delicate  bits  of  loose  cotton  and  they 
will  rush  toward  it,  and  remain  for  a  little  time  clinging 
to  it.     These  various  effects  show  the  presence  of  elec- 
tricity :  the  friction  of  the  flannel  upon  the  glass  has 
produced  it. 

2.  The  electrical  machine. — The  electrical  machine 
is  an  apparatus  for  producing  electricity  by  friction. 
It  is  represented  in  Fig.  124.     Its  principal  parts  are, 
1st,  a  body  upon  whose  surface   electricity  is  to  be 
evolved ;  2d,  the  rubber  by  the  friction  of  which  elec 
tricity  is  produced  ;  and  3d,  the  conductor  on  which 
the   electricity  may   be   accumulated.      In  the  form 
shown  by  the  figure,  the  first  of  these  parts  consists  of 
a  thick  glass  plate  P,  to  be  turned  by  a  crank.     The 
rubber  B.  is  made  of  leather,  covered  with  an  amal- 
gam made  of  mercury,  tin,  and  zinc.    Two  such  pieces 
of  leather  are  pressed,  one  against  each  side  of  the 
plate,  by  means  of  a  brass  clamp,  which  is  supported 


253  NATURAL    PHILOSOPHY. 

upon  a  glass  pillar.    The  conductor,  or  as  usually  called 
the  prime  conductor,  C,  is  a  brass  ball,  or  a  cylinder 
with  rounded  ends,  mounted  on  a  glass  support.     Con- 
Fig.  124. 


nected  with  the  prime  conductor,  is  a  brass  fork  F,  one 
prong  of  which  is  on  each  side  of  the  plate,  with  many 
sharp  projecting  points  reaching  toward  the  glass. 

By  turning  the  crank,  the  friction  of  the  rubber  upon 
the  plate  evolves  electricity,  which  remains  upon  the 
surface  of  the  glass  until  it  is  brought  around  to  the 
fork :  it  is  there  taken  by  the  points,  and  it  passes  over 
the  prongs  to  spread  itself  over  the  surface  of  the  prime 
conductor.  The  glass  support  prevents  it  from  leaving 
the  conductor.  When  the  machine  is  in  operation  the 
rubber  is  connected  with  the  floor  by  a  chain.  All 
parts  of  the  machine  must  be  free  from  dust  and 
thoroughly  dry.  * 


NATURAL    PHILOSOPHY'.  353 

When  a  machine  of  this  kind,  of  medium  size,  is  in 
successful  operation,  the  effects  of  the  glass  tube  are 
experienced  in  a  far  greater  degree.  The  face  or  the 
back  of  the  hand  will  feel  the  breezy  or  prickling  sen- 
sation at  a  distance  of  several  inches  from  the  conduct- 
or :  all  light  bodies  held  near  it,  immediately  fly  to  its 
surface,  and  if  the  knuckle  or  a  brass  ball  be  brought 
near,  bright  and  zigzag  sparks  may  be  drawn  through 
a  distance  of  from  one  to  two  inches,  the  light  being 
accompanied  by  a  sharp  report. 

3.  Electricity  detected  by  electroscopes. — When  the 
force  of  the  electricity  is  slight,  there  should  be  some 
convenient  way  of  showing  its  presence.     Any  instru- 
ment for  this  purpose  is  called  an  electroscope.     The 
simplest  form  is  called  the  pith-ball  electroscope.     It 
consists  (see  Fig.  125)  of  a  bail  of  pith  from  the  corn- 
stalk, or  elder,  hung  by  a  slender  silk  thread  from  a 
glass  support     This  little  ball  will  instantly    Fi<r  .,25 
announce  the  presence  of  electricity  by  moving 
toward  the  body  which  contains  it. 

4.  Two  opposite  forces. — Electricity  shows 
its  presence  both  by  attraction  and  repulsion, 
for   if  the  pith-ball   of  the  electroscope   be 
brought  near  to  the  prime  conductor  of  the 
electrical  machine,  it  will  fly  toward  it,  but 
on  coming  in  contact  with  it,  will  as  instantly 
leap  away  again. 

Now,  rub  a  glass  rod  with  flannel,  and 
hold  it  near  the  pith-ball  which  has  been  repelled  by 
the  conductor ;  the  glass  rod  will  also  repel  it ;  but  if 
a  stick  of  sealing-wax  be  used  in  place  of  the  glasa 
tube,  the  pith-ball  will  be  strongly  attracted.  Notice, 
that  the  pith-ball  i8  repelled  by  the  electricity  of 


254  NATURAL    PHILOSOPHY. 

glass,  and  attracted  by  the  electricity  of  sealing-wax. 
It  is  thus  seen  that  the  electricities  of  glass  and  sealing- 
wax  are  not  alike.  To  distinguish  them  from  each 
other,  that  which  is  produced  on  glass  by  the  friction 
of  flannel  is  called  positive  electricity ;  that  produced 
apor  sealing-wax  is  called  negative  electricity. 

It  is  found  to  be  impossible  to  develop  one  of  these 
forces  without  the  other  also.  The  positive  force 
always  appears  on  one  of  the  bodies  rubbed  together, 
and  the  negative  upon  the  other. 

5.  The  forces  measured  by  electrometers. — The  sim- 
plest form  of  the  electrometer  is  represented  in  Fig. 
126.  It  consists  of  a  brass  standard,  with  a  graduated 
semicircle,  on  the  center  of  which  moves 
an  index  of  very  -light  wood,  carrying  a 
pith-ball  at  its  lower  end.  When  not  in 
use,  the  pith-ball  hangs  in  contact  with 
the  standard,  but  when  the  standard  is 
brought  near  to  an  electrified  body,  the 
pith-ball  is  instantly  repelled.  The  arc 
through  which  it  moves  is  taken  as  the 
measure  of  the  force.  (See  Silliman's  Phys., 
p.  538.) 

6.  The  first  law. — We  have  seen  that 
positive  electricity  is  produced  by  friction 
on  glass,  and  that  the  opposite  force  is  evolved  by  fric 
tion  on  sealing-wax.  Now,  let  two  pith-balls  be  sus- 
pended by  silk  threads  so  as  to  be  in  contact.  Thoroughly 
rub  the  glass  tube ;  bring  it  in  contact  with  the  balls ; 
they  both  receive  positive  electricity  from  the  tube,  and 
it  will  be  found  that  they  will  no  longer  remain  in  contact. 
We  learn  from  this  experiment  that  two  bodies  with 
the  same  kind  of  electricity  repel  each  other. 


NATURAL    PHILOSOPHY.  255 

Again:  let  the  sealing-wax  be  thoroughly  rubbed 
and  brought  near  to  the  two  pith-balls  while  they  are 
repelling  each  other,  and  they  will  both  fly  toward  it. 
We  learn  from  this  experiment  that  bodies  with  dif- 
ferent kinds  of  electricity  attract  each  other. 

This  law  furnishes  an  easy  test  by  which  to  find 
out  which  kind  of  electric  force  is,  in  any  case,  produced. 
Is  the  prime  conducter  of  the  electrical  machine  positive 
or  negative  ?  To  decide  this  question,  rub  the  glass 
tube;  bring  it  in  contact  with  the  pith-ball  of  the 
electroscope  ;  the  electricity  of  the  ball  is  thus  known 
to  be  positive.  Now,  bring  it  near  the  prime  conduct- 
or of  the  machine  in  operation;  it  is  repelled.  The 
electricity  of  the  conductor  is  positive.  The  electricity 
of  the  rubber  is  negative,  because,  if  the  chain  be  re 
moved,  and  the  electrified  pith-ball  be  brought  near 
the  brass  mounting  of  the  rubber  post,  it  will  be 
attracted. 

7.  The  second  law. — If  the  standard  of  the  electrom- 
eter be  brought  in  contact  with  an  electrified  body, 
the  index  will  be  thrown  along  the  graduated  arc 
to  a  greater  or  less  distance,  as  the  electric  force  ia 
stronger  or  weaker.  By  carefully  conducted  experi- 
ments, these  distances  may  be  compared,  and  it  is 
found  that  the  strength  or  intensity  of  the  force  is  in- 
versally  as  the  square  of  the  distance.  The  attraction 
of  the  prime  conductor  for  a  body  at  a  distance  of  two 
inches  is  only  J  as  strong  as  at  a  distance  of  one  inch. 

(91.)  A  charged  or  electrified  body,  acting  through  a 
non-conductor  upon  an  insulated  conductor,  polarizes  it. 
This  action  is  called  induction. 

1.  A  charged  body. — Whenever  by  friction,  electricity 


256  NATURAL    PHILOSOPHY. 

is  developed  upon  the  surface  of  a  body,  the  bodj  is 
said  to  be  electrified,  and  if,  by  bringing  another 
body  in  contact  with  it,  electricity  is  imparted,  the 
body  which  receives  it  is  said  to  be  charged.  Thus, 
the  glass  tube,  when  rubbed,  becomes  electrified ;  the 
pith-ball  of  the  electroscope,  coming  in  contact  with 
the  glass,  takes  electricity  from  it  and  becomes 
charged. 

2.  A  non-conductor. — Some  bodies  allow  electricity 
to  pass  freely  over  their  surfaces ;  such  bodies  are  called 
conductors :  'others  will  not  allow  electricity  to  pass 
freely  over  them  ;  these  are  called  non-conductors.     If 
a  brass  rod  be  held  in  contact  with  the  prime  conductor 
of  a  machine,  it  will  be  found  impossible  to  charge  it ; 
a  glass  rod  held  in  the  same  way,  will  not  prevent  the 
charge  from  accumulating.     The  brass  allows  the  elec- 
tricity to  pass  into  the  person ;  the  glass  does  not :  brass 
is  a  conductor ;  glass  is  a  non-conductor.     The  metals, 
as  a  class,  are  good  conductors.   Beside  glass,  we  notice 
silk,  india  rubber,  and  dry  air,  as  being  among  the  best 
non-conductors. 

3.  An  insulated  ~body. — Whenever  a  body  is  quite 
surrounded  by  non-conductors,  it  is  said  to  be  insulated. 
The  conductor  of  the  machine  is  insulated  by  resting 
upon  a  glass  support.     A  body  which  is  not  insulated 
can  not  be  charged. 

4.  A  charged  body  polarizes  an  insulated  conductor. 
— A  body  is  said  to  be  polarized  when  the  two  opposite 
electricities  both  exist  upon  its  surface     To  illustrate 
this  important  condition,  let  an  insulated  metallic  ball 
be  connected  with  the  prime  conductor  of  the  electrical 
machine,  and  let  a  small  insulated  conductor  be  placed 
near  it  (see  Fig.  127).    When  the  ball  is  charged,  the 


NATURAL    PHILOSOPHY.  251 

motion  of  the  pith -balls  fastened  to  the  small  conductor, 
shows  that  it  is  also  charged,  and  if  its  electricity  be 
tested,  it  will  be  found  to  be  positive  at  one  end  and 
negative  at  the  other.  Both  elec-  Fig.  127. 

tricities  are  developed  upon  its  sur-          K       .       ,       k 
face  at  the  same  time,  and  the  body 
is  said  to  be  polarized.     The  ac- 
tion of  the  ball,  by  which  this  body 
is  polarized,  is  called  induction. 

If  we  examine  the  condition  of  the  polarized  body 
more  carefully,  we  find  that  in  the  end  next  to  the 
ball  there  is  negative  electricity,  and  in  the  distant  end 
there  \s>  positive  electricity.  This  is  always  true  :  when  a 
body  is  electrified  by  induction,  the  end  or  side  nearest 
the  charged  body  is  always  in  a  condition  opposite  to 
that  which  develops  it. 

When  the  insulated  conductor  is  near  to  the  ball, 
the  induction  is  strong :  the  greater  the  distance  be- 
tween them,  the  weaker  it  becomes,  until,  at  a  certain 
distance,  it  can  no  longer  be  detected. 

If,  when  the  conductor  is  polarized,  one  end  be 
touched  with  the  finger,  the  entire  surface  remains 
charged  with  the  opposite  electricity.  It  will  remain 
charged,  even  when  taken  beyond  the  influence  of  the 
body  which  polarized  it. 

(92.)  A  series  of  insulated  conductors,  placed  end  to 
end,  near  each  other,  may  be  all  polarized  by  bringing 
a  charged  body  near  to  one  of  them.  Faraday's  theory 
explains  induction  by  supposing  the  molecules  of  a  body 
to  be  polarized  from  each  other  in  the  same  way. 

1.  A  series  of  conductors  polarized. — Let  a  number 
of  small  insulated  conductors  be  placed  end  to  end, 


258  NATURAL    PHILOSOPHY. 

near  together,  with  one  end  of  the  first  one  near  to 
Fig.  128.  a  brass  hall  connected 

with  the  prime  con- 
ductor of  the  machine 
(see  Fig.  128).  The 
motion  of  the  pith- 
balls  will  show  that 
they  are  all  polarized.  The  effect  will  be  greater  if 
another  brass  ball,  connected  with  the  rubber  of  the 
machine,  is  placed  at  the  other  end  of  the  series.  The 
positive  and  negative  electricities  are  on  opposite  ends 
of  each  conductor.  All  the  ends  toward  the  positive 
ball  are  negative;  all  the  ends  in  the  other  direction 
are  positive. 

2.  The  Theory  of  Induction. — Now  the  molecules  of 
one  of  these  conductors  are  as  truly  separate  bodies  as 
v,he  conductors  themselves,  and  as  one  electrified  con- 
ductor may  polarize  another,  so  one  of  these  molecules, 
acting  through  the  minute  distance  between  them,  may 
polarize  another.  This  polarizing  influence  passes  from 
one  molecule  to  another,  until  all  the  molecules  of  the 
body  are  thrown  into  this  condition,  each  molecule  hav- 
ing opposite  electricities  on  its  opposite  sides. 

The  theory  goes  further,  and  supposes  that  the  mole- 
cules of  conductors  discharge  their  forces  easily  into  one 
another,  while  those  of  non-conductors  do  not.  For 
this  reason,  the  molecules  of  the  air  between  the  charged 
ball  and  the  end  of  the  conductor  are  polarized  and 
retain  their  electricities,  while  the  molecules  of  the  con 
ductors,  as  fast  as  they  are  polarized,  give  their  electric 
forces  to  their  neighbors.  The  positive  force  given  from 
one  to  another,  in  one  direction,  accumulates  at  one  end 
of  the  conductor ;  the  negative  force,  given  from  one  to 


NATURAL    PHILOSOPHY.  25JJ 

another  in  the  other  direction,  accumulates  at  the  other 
end. 

(93.)  The  Leyden-jar  is  an  apparatus  for  accumulat- 
ing electricity  by  induction.  It  may  be  charged  by 
bringing  one  of  its  coatings  in  contact  with  a  charged 
body,  the  other  being  in  contact  with  conductors.  It 
may  be  discharged  by  making  a  conducting  communi- 
cation between  its  two  coatings.  The  Leyden  battery 
consists  of  several  Leyden-jars  connected. 

1.  The    Leyden-jar.— The    Leyden-jar    (Fig.    129) 
consists  of  a  glass  jar,  coated  both  inside      rig.  129. 
and  outside  with  tin-foil,  to  within  a  few 

inches  of  the  top,  and  provided  with  a  cov- 
er of  hard  dry  wood,  through  which  passes 
a  brass  rod,  with  a  ball  upon  its  upper  end, 
and  a  chain  reaching  from  its  lower  end  to 
the  bottom  of  the  jar. 

It  will  be  seen  by  this  description,  that 
in  this  instrument  there  are  two  conducting 
surfaces,  separated  from  each  other  by  a 
non-conductor. 

This  idea  may  be  embodied  in  a  variety  of  forms,  any 
one  of  which  will  act  on  the  principle  of  the  Leyden- 
jar.  Thus  a  pane  of  glass,  coated  with  tin-foil  on  both 
Bides,  to  within  a  little  distance  of  the  edge  all  around, 
has  the  essential  parts  of  the  Leyden-jar.  A  glass  gob 
"let  partly  full  of  water  and  grasped  by  the  hand,  illus-^ 
trates  the  same  idea  :  the  glass,  a  non-conductor,  sepa- 
rates two  conducting  surfaces — the  water  on  the  inside, 
and  the  hand  upon  the  outside. 

2.  It  may  ~be  charged. — By  bringing  the  ball  of  the 
Leyden-jar  in  contact  with  the  prime  conductor  of  the 


260  NATURAL    PHILOSOPHY. 

machine,  positive  electricity  passes  into  the  inside  coat- 
ing. This  positive  electricity  polarizes  the  outside 
coating,  causing  its  surface  next  the  glass  to  be  nega- 
tive, and  the  other  to  be  positive.  If  in  contact  with  a 
conductor,  this  positive  electricity  will  pass  off,  and 
thus  leave  the  outside  coating  permanently  charged  with 
negative  electricity.  When  by  this  action  the  two  coat- 
ings have  opposite  electricities,  the  jar  is  said  to  be 
charged.  It  may  be  removed  from  the  prime  conduct- 
or and  remain  charged,  because  the  two  forces  hold 
each  other  by  acting  through  the  glass.  The  jar  may 
be  handled  without  danger,  if  care  be  taken  not  to 
touch  the  ball  and  the  outside  at  the  same  time. 

The  jar  is  charged  with  positive  electricity  when  that 
force  is  upon  the  inside ;  it  is  charged  with  negative 
electricity  when  negative  force  is  upon  the  inside. 

3.  It  may  ~be  discharged. — When  a  conducting  com 
munication  is  made  between  the  two  coatings  of  the  jar, 
the  two  opposite  forces  come  together,  neutralize  each 
other,  and  the  jar  is  said  to  be  discharged.  The  con 
ducting  communication  may  be  made  in  many  ways 
The  discharger  is  a  convenient  instrument  for  the  pur- 
pose. It  consists  of  two  bent  brass  arms,  with  a  ball 
upon  one  end  of  each,  the  other  ends  being  fastened  by 
a  joint  to  a  glass  handle.  Taking  hold  of  the  glass 
handle,  bring  one  ball  in  contact  with  the  outside  of  the 
jar,  and  the  other  near  to  the  knob ;  a  bright  spark  and 
a  sudden  report  announce  the  discharge. 

The  coated  glass  plate  and  the  goblet  of  water,  men- 
tioned before,  may  be  charged  and  discharged  in  the 
same  way  as  a  Leyden  jar.  To  charge  the  goblet,  for 
example,  let  a  chain  from  the  prime  conductor  of  the 
machine  hang  into  the  water ;  grasp  the  outside  of  the 


NATURAL    PHILOSOPHY.  261 

while  the  machine  is  in  operation.  Positive  elec- 
tricity will  be  given  to  the  water ;  negative  electricity 
will  be  induced  upon  the  hand,  and  the  goblet  is  thus 
charged.  Now  with  the  other  hand  try  to  remove  the 
chain  :  the  moment  the  chain  is  touched,  a  slight  shock 
will  be  felt,  announcing  the  discharge  which  occurs. 

4.  Tfie  Ley  den  lattery. — The  larger  the  surface  of 
the  coatings  of  the  jar,  the  more  powerful  will  be  the 
chaige  accumulated.  We  can  obtain  a  larger  surface 
by  using  a  larger  jar,  or  it  may  be  done  by  taking  sev- 
eral small  ones  and  joining  their  surfaces  by  conductors. 
In  the  last  case,  the  Leyden  battery  will  be  formed. 
When  the  inside  surfaces  are  all  connected  by  conduct- 
ors reaching  from  knob  to  knob,  and  the  outsides  all 
joined  by  standing  the  jars  on  a  metallic  surface,  the 
battery  may  be  charged  and  discharged  as  a  single  jar. 
It  is  equivalent  to  a  single  jar  large  enough  to  have  the 
same  extent  of  surface.  -^ 

^  (94.)  The  electricity  of  the  atmosphere  is  of  the  same 
nature  as  that  produced  by  friction.  Lightning  is  the 
discharge  of  oppositely  charged  clouds,  illustrating,  on 
a  grand  scale,  the  action  of  a  Ley  den -jar. 

The  aurora  is  doubtless  produced  by  electric  dis- 
charges taking  place  in  the  rarefied  air  of  the  upper 
portions  of  the  atmosphere. 

1.  Electricity  of  the  atmosphere. — The  atmosphere  is 
very  generally  in  an  electrified  condition.  This  may 
be  shown  by  raising  a  metallic  rod  to  a  considerable 
height  above  the  ground,  having  an  electroscope  fast- 
ened to  its  lower  end,  which  should  be  insulated.  A 
sensitive  electroscope  will  usually  indicate  positive  elec- 
tricity, its  intensity  increasing  as  the  air  from  which  it 


262  NATURAL    PHILOSOPHY 

is  drawn  is  higher.  In  its  ordinary  state,  the  electricity 
of  the  atmosphere  is  always  positive :  stronger  in  win- 
ter than  in  summer,  and  during  the  day  than  the  night. 
In  cloudy  weather  the  electrical  state  is  uncertain,  some- 
times changing  from  positive  to  negative  and  back 
again  in  a  few  minutes.  On  the  approach  of  a  thunder- 
storm these  changes  follow  each  other,  at  times,  with 
remarkable  swiftness. 

2.  It  is  of  the  same  nature  as  frictional  electricity. 
— The  bright  flash  and  loud  report  which  announce  the 
discharge  of  a  Leyden-jar  or  battery,  can  not  have 
failed  to  remind  one  who  has  observed  them,  of  the 
brighter  flash  and  louder  report  of  atmospheric  light- 
ning and  thunder.  These  grand  and  sometimes  awful 
displays  of  electricity,  are  caused  by  the  same  agent 
which,  produced  on  a  glass  tube,  lightly  pricks  the 
cheek  or  attracts  a  pith-ball. 

To  Dr.  Franklin  belongs  the  immortal  honor  of  prov- 
ing the  identity  of  electricity  and  lightning.  A  kite 
was  the  simple  instrument  employed  by  this  man  of 
genius.  Having  made  a  kite  by  stretching  a  silk  hand- 
kerchief over  two  sticks  in  the  form  of  a  cross,  he  went 
out  into  a  field,  accompanied  only  by  his  son :  raised  his 
kite ;  fastened  a  key  to  the  lower  end  of  its  hempen 
string;  insulated  it  by  fastening  it  to  a  post  by  means  of  a 
silk  cord,  and  anxiously  awaited  the  approaching  storm. 
A  dense  cloud,  apparently  charged  with  lightning,  soon 
passed  over  the  spot  where  he  stood,  without  causing 
his  apparatus  to  give  any  sign  of  electricity.  He  was 
about  to  give  up  in  despair,  when  he  caught  sight  of 
some  loose  fibers  of  the  hempen  cord,  bristling  up  as  if 
repelled.  He  immediately  presented  his  knuckle  to 
the  key,  and  received  an  electric  spark.  The  string  of 


NATURAL    PHILOSOPHY".  263 

his  kite  soon  became  wet  with  the  falling  rain  ;  it  was 
then  a  better  conductor,  and  he  was  able  to  obtain  an 
abundance  of  sparks  from  the  key.  By  this  experiment 
he  furnished  a  decisive  proof  of  the  identity  of  light- 
ning and  electricity. 

3.  Lightning  is  the  discharge  of  oppositely  charged 
clouds. — Clouds   are   often    charged   with   electricity. 
When  two  of  them,  with  opposite  kinds  of  electricity, 
come  near  enough  together,  they  will  act  like  the  two 
charged  coatings  of  the  Ley  den-jar,  the  air  between  them 
being  a  non-conductor  like  the  glass.    When  the  charge 
rises  high  enough,  a  discharge  takes  place :  the  spark 
of  the   discharge   being   a  flash  of  lightning,  and  its 
report  a  thunder  peal.     Considering  the  large  extent 
of  cloud  surfaces  discharged,  we  need  not  be  surprised 
at  the  magnitude  of  the  spark,  nor  at  the  deep  intensity 
of  the  sound. 

When  the  discharge  is  not  hidden  by  clouds,  we  can 
trace  the  whole  length  of  the  spark,  and  we  witness 
chain-lightning  •  but  at  other  times  the  spark  is  behind 
the  clouds;  we  see  only  the  light  of  the  discharge 
spread  over  the  surface  of  the  clouds,  and  this  gives 
rise  to  what  is  called  sheetrlightning. 

At  times  the  earth  and  a  cloud  are  the  two  charged 
surfaces,  and  a  discharge  takes  place  between  them. 
Such  discharges  are  the  source  of  danger  to  life  and 
property.  Animals,  trees,  buildings,  all  these  are 
better  conductors  than  air,  and  electricity  always 
chooses  the  best  conductors  in  its  passage.  In  going 
from  a  cloud  to  the  earth  it  takes  these  bodies  in  its 
way;  animals  are  often  killed,  trees  shattered,  and 
buildings  torn  to  pieces  or  set  on  fire. 

4.  The  aurora. — This  curiously  beautiful  phenomenon 


264:  NATURAL    PHILOSOPHY. 

consists  of  a  diffuse  light,  somewhat  like  the  morning 
or  the  evening  twilight,  seen  in  the  northern  sky.  It 
exhibits  a  great  variety  of  appearances.  Sometimes  it 
looks  much  like  the  dawn  of  morning  seen  in  the  north 
instead  of  the  east.  Sometimes  it  takes  the  form  of  an 
arch,  like  a  rainbow,  but  without  its  colors.  At  other 
times  slender  columns  of  delicate  light,  pointing  up- 
ward from  the  northern  horizon,  not  always  stationary, 
but  often,  on  the  contrary,  leaping  up  and  down  with 
swift  and  varied  motions,  as  if  engaged  in  a  merry 
dance. 

In  the  southern  hemisphere  an  aurora  is  also  seen  in 
the  southern  horizon.  To  distinguish  these  two  auro 
ras,  that  in  the  north  has  been  called  the  aurora  'bore- 
alls,  while  that  in  the  south  is  the  aurora  austmlis. 

5.  It  is  produced  by  electric  discharges  in  rarefied 
air. — There  is  still  much  uncertainty  about  the-  cause 
of  the  aurora,  but  late  investigations  leave  no  doubt  as 
to  its  electrical  nature.  From  all  the  facts  gathered,  it 
seems  to  consist  of  beams  or  discharges  of  electricity, 
between  the  earth  and  the  upper  regions  of  the  atmos- 
phere. 

When  electricity  discharges  through  air  of  the  usual 
density,  it  takes  the  form  of  a  spark,  the  light  being 
intense  and  nearly  white.  If  passed  through  a  glass 
vessel,  in  which  the  air  is  rarefied,  the  light  is  more 
diffuse  and  tinged  with  a  rosy  hue.  If  the  air  be 
still  further  rarefied,  the  light  becomes  very  diffuse, 
spreads  readily  through  a  great  distance,  and  its  color 
becomes  a  deep  rose  or  purple. 

Now  the  air  of  the  upper  atmosphere  is  much  rare- 
fied, and  we  should  infer  that  electric  discharges  there 
would  give  a  diffuse  light  of  various  colors.  Such  is 


NATURAL    PHILOSOPHY.  265 

the  observed  character  of  the  aurora.    (See  Smithsonian 
Report,  1865,  p.  208.) 

(95.)  A  body  having  points  projecting  from  its  sur- 
face can  not  be  charged  even  when  insulated.  Or  if  a 
pointed  conductor  be  held  toward  its  surface  it  will 
prevent  a  charge  from  accumulating,  by  drawing  the 
force  away  silently.  Upon  this  principle,  buildings  are 
protected  from  the  effects  of  lightning  by  lightiiing- 
rods. 

1.  The  effect  of  points. — It  is  found  to  be  impossible 
to  charge  a  conductor  when  there  are  sharp  points  on 
its  surface,  or  held  near  to  it.  To  illustrate  this  curious 
effect  of  points,  fasten  a  pointed  wire  to  the  prime  con- 
ductor of  the  electrical  machine,  and  the  sparks,  which 
before  couid  be  drawn  from  it  in  abundance,  cease 
altogether,  and  even  pith-balls  fail  to  detect  the  pres- 
ence of  the  force.  Or  take  the  pointed  wire  in  the 
hand  and  present  its  point  to  the  prime  conductor, 
within  a  few  inches  of  its  surface ;  not  a  spark  can  be 
drawn  from  it,  nor  will  the  pith-balls  show  either  at- 
traction or  repulsion.  The  discharge  is  silently  effected 
by  the  air  in  front  of  the  points.  Its  molecules  become 
polarized,  and  are  first  attracted  to  the  point  and  then 
repelled.  On  coming  in  contact  with  the  point,  they 
take  electricity  from  it  and  move  away :  others  being 
polarized  are  attracted,  receive  electricity,  and  pass 
away.  Thus  the  electricity  of  the  body  is  silently 
carried  off  from  the  point.  That  such  currents  of  air 
do  really  exist,  may  be  proved  by  various  experiments. 
1  f,  for  example,  the  cheek,  or  the  back  of  the  hand,  be 
held  near  to  the  point,  the  breeze  will  be  felt :  or  if  the 
small  flame  of  a  lighted  taper  be  held  just  in  front  of 
12 


NATURAL    PHILOSOPHY. 

the  point  on  the  prime  conductor,  it  will  be  blown  away 
from  it,  and  may  even  be  extinguished. 

The  discharge  takes  place  from  the  point  because  the 
charge  being-  more  intense  there  than  elsewhere,  the 
polarization  of  the  air  is  greater  there  than  at  any 
other  part  of  the  body. 

2.  Lightning-rods.-  W«  ]mve  seen  that  because 
buildings  are  better  conductors  of  electricity  than  air, 
they  are  liable  to  injury  from  strokes  of  liglVning. 
when  the  discharge  takes  place  between  the  cloud  and 
the  earth.  But  since  pointed  conductors  silently  dis- 
charge the  force  from  a  charged  body,  why  not  disarm 
the  cloud  of  its  lightning  by  the  use  of  pointed  metallic 
rods  ?  This  question  was  no  sooner  suggested  to  the 
practical  mind  of  Franklin,  than  a  trial  was  made, 
which  verified  his  bold  conjecture. 

Conductors  for  the  purpose  of  protecting  buildings 
»*m  the  effect  of  lightning,  are  called  lightning- 
''ods.  They  should  be  made  of  metallic  rods,  pointed 
•i  the  upper  end,  reaching  several  feet  above  the  high- 
est part  of  the  building  which  they  are  designed  to 
protect,  and  downward,  without  interruption,  into  the 
ground  below  its  foundation. 

(96.)  The  effects  of  frictional  electricity  are  mechani- 
cal, chemical,  and  physiological. 

1.  Mechanical  effects. — We  have  already  had  abund- 
ant illustrations  of  motions  caused  by  the  electric 
forces.  Poor  conductors  are  also  pierced  or  torn  by 
Ihe  electric  discharge.  To  illustrate  this  by  experiment, 
let  the  charge  of  a  Ley  den-jar  be  passed  through  a  piece 
of  card-board  ;  the  card  will  be  pierced  with  a  burred 
01  ragged  perforation.  This  effect  is  produced  on  a 


NATURAL    PHILOSOPHY.  267 

»arge  scale  by  the  lightning  stroke;  even  rocks  are 
sometimes  shattered,  while  trees  are  often  splintered 
from  top  to  root,  and  their  fragments  scattered  far  and 
near  in  all  directions. 

2.  Chemical  effects. — The  chemical  effects  of  electri- 
city are  shown  through  the  agency  of  the  heat  which 
it  develops.     To  illustrate  by  experiment  :  wrap  the 
ball  of  a  Leyden-jar  with  loose  cotton,  and  sprinkle 
upon   this,  very  finely  powdered   resin.     This   done, 
charge  the  jar  powerfully,  and  then  discharge  it  by 
bringing  first  one  ball  of  the  discharger  in  contact  with 
the  outside  of  the  jar,  and  then  the  other  a  little  above 
its  hooded  knob.     The  discharge  takes  place  through 
the  resin,  and  sets  it  on  fire.     Buildings  are  sometimes 
set  on  fire  by  the  lightning-stroke. 

3.  Physiological  effects. — The    effect  of   electricity 
upon  the  human  system  is  peculiar  and  startling.     !N"o 
description  can  give  a  correct  idea  of  it :  it  must  be  ex- 
perienced by  one  who  would  know  what  it  is.     Let  a 
person  place  one  han«t   upon  the  outside  surface  of  a 
lightly  charged    Leyden-jar,  and  with  the  other  hand 
touch  its  knob.    He  will  find  that  his  own  will  can  no 
longer  control  his  muscles  :  his  hands  are,  on  the  in- 
stant, suddenly  jerked,  while  a  peculiar  and  almost 
indescribable  sensation  is  felt  in  the  wrists  and  arms. 

Many  persons  by  joining  hands  may  form  an  un- 
broken connection  between  the  two  coatings  of  the  jar, 
and  at  once  experience  these  effects. 

»- 

§    2.    OF    MAGNETIC    ELECTRICITY. 

(97.)  Magnets  are  either  natural  or  artificial,  and 
may  be  made  in  different  forms ;  but  in  any  form  the 


2G8  NATURAL    PHILOSOPHY. 

magnetism  is  stronger  at  the  ends  than  in  the  middle. 
The  ends  are  called  poles. 

1.  Magnets. — Bodies  that  attract  iron  in  preference 
to  other  metals,  are  called  magnets.     They  are  usually 
made  of  steel.     To  illustrate  their  peculiar  preference 
for  iron,  let  some  iron  filings  be  mixed  with  some  filings 
of  brass;  bring  one  end   of  the   magnet   among  the 
filings,  and  on  removing  it,  great  numbers  of  the  iron 
particles  will  be  seen  clinging  to  it,  while  the  brasa 
particles  are  all  left  behind. 

2.  The  natural  magnet.  —Fragments  of  an  ore  of 
iron  are  sometimes  found  which  have  the  properties  of 
a  magnet.      Such  a  fragment  is  a  natural  magnet  or 
loadstone. 

3.  The  artificial  magnet. — If  a  bar  of  iron  or  steel 
be  rubbed  against  a  magnet  it  will  become  magnetic ; 
it  will  then  be  an  artificial  magnet.  "Whether  it  remains 
magnetic  for  any  length   of  time   depends  upon  its 
hardness.       Soft  iron  or  steel  will  lose  its  magnetic 
properties  quickly  ;   hardened  iron  or  steel  will  retain 
them. 

4:.  They  are  made  in  different  forms. — The  two  most 
important  forms  of  magnet  are  the  straight  or  "bar 
magnet,  and  the  horseshoe  magnet.  These  names  are 
descriptive  :  the  bar  magnet  is  a  straight  bar  of  steel , 
the  horseshoe  magnet  is  a  magnet  whose  shape  is  that 
of  a  horseshoe,  or  the  letter  TJ;  its  ends  are  thus  brought 
aear  together. 

5.  Their  force  is  stronger  at  their  ends. — If  a  bar 
magnet  be  rolled  in  a  bed  of  iron  filings,  large  clusters 
of  them  will  be  found  clinging  to  its  ends,  their  num- 
bers getting  loss  toward  the  middle  of  the  bar,  where 
very  few,  if  any,  will  be  held/  By  this  experiment  we 


NATURAL    PHILOSOPHY.  2(59 

learn  that  the  magnetic  forces  are  not  equally  distrib- 
uted over  the  surfaces  of  magnets,  but,  on  the  contrary, 
that  they  are  strong  at  the  ends  and  weak  or  neutral  in 
the  middle.  The  ends  are  called  poles,  one  being  a 
north  pole,  the  other  a  south  pole. 

(98.)  Magnetism  shows  itself  both  by  attraction  and 
repulsion,  obeying  the  following  law:  poles  of  like 
names  repel  each  other;  those  of  different  namea 
attract. 

1.  Attraction  and  repulsion. — Iron   which    is    not 
magnetic  will  be  attracted  equally  by  both  poles  of  a 
magnet ;  it  is  not  so  when  two  magnets  act  upon  each 
other.     By  presenting  one  end  of  a  magnet  to  the  north 
pole  of  another,  it  will  show  an  attraction  for  it,  while 
the  other  end  being  presented  to  the  same  pole  will  re- 
pel it.     Thus  magnetism,  like  electricity  by  friction, 
shows  itself  by  both  attraction  and  repulsion. 

2.  The  law. — When   we  examine  the  subject  more 
closely,  we  find  that  magnetic  attraction  and  repulsion 
is  also  governed  by  the  same  law  as  electricity.     Thus, 
if  we  bring  the  north  poles   of  two  magnets  near  to 
each   other,  they  repel   each   other :   two  south  poles 
manifest  the  same  effect.     But  if  we  bring  a  north  pol* 
near  to  a  south  pole,  an  attraction  instantly  springs  up 
between  them,  and  if  allowed  to  touch  each  other  they 
will  cling  together :  one  may  even  lift  the  other  by  the 
strength  of  the  attraction.     It  is  evident  from  these 
simple  experiments  that  poles  of  the  same  name  repel, 
while  those  of  opposite  names  attract  each  other. 

(99.)  A  magnet,  like  a  charged  body,  will  polarize  a 
bar  of  iron  brought  near  to  one  of  its  poles,  always  in- 


270  NATURAL    PHILOSOPHY 

ducing  magnetism  of  the  opposite  kind  in  the  end  next 
to  it.  The  polarizing  influence  may  extend  through 
Be^  eral  bars  placed  end  to  end. 

It  is  supposed  that  every  molecule  of  a  magnet  is  in 
a  polarized  state,  the  north  polarity  being  on  the  same 
side  of  them  all,  and  the  south  polarity  on  the  other 
Bids. 

1.  A  magnet  will  polarize  a  "bar  of  iron. — If  a  bar  of 
iron  n  s  and  a  magnet  N  S  (Fig.  130),  be  placed  end 

Fig.   to  end,  the  iron  itself  becomes  a  magnet.     That 
18°*    it  is  a  magnet  may  be    shown    by  its   power  to 
attract  or  repel  the  poles   of    another  magnet 
Both  kinds  of  magnetism  are  developed  in   it, 
and  hence  we  call  it  polarized. 

If  now,  we  examine  more  carefully,  we  notice 
that  one  end  of  the  bar  is  near  the  south  pole  of 
the  magnet,  and  we  find  by  experiment,  that  the 
opposite  end  is  likewise  a  south  pole.  Hence, 
that  end  of  the  bar  next  to  the  magnet  must  be 
S  a  north  pole.  Each  pole  of  a  magnet  will  always 
in  this  way  induce  the  opposite  kind  of  magnetism  in 
that  end  of  the  bar  nearest  to  it. 

Unlike  frictional  electricity,  there  is  no  discharge 
of  magnetism  when  opposite  kinds  are  brought  to- 
gether :  the  polarization  takes  place  even  when  the 
bar  is  in  contact  with  the  magnet,  and  if  the  bar  be 
made  of  steel,  the  polarity  remains  after  the  magnet  ia 
removed. 

2.  Several  bars  may  "be polarized. — A  second  bar  may 
be  A?laced  with  one  end  near  to  the  first,  and  be  found 
tc  be  polarized ;  so  a  third  may  be  polarized  by  the 
second:  the  series  may  be  continued  further,  but  the 
force  is  less  in  each  successive  magnet.     To  illustrate 


NATURAI     PHILOSOPHY.  271 

by  experiment :  from  the  north  pole  of  a  strong  bar 
magnet,  hang  a  key,  from  the  lower  end  of  this  one  a 
smaller  key  may  be  hung,  a  third  still  smaller  will  be 
held  by  this,  and  a  tack  will  cling  to  the  lower 
end  of  the  last.  The  series  of  keys  and  nails 
has  become  a  series  of  magnets,  each  with  its 
north  and  south  pole,  their  north  poles  all  di- 
rected downward  (see  Fig.  131). 

3.  All  the  molecules  of  a  magnet  are  polar- 
ized.— Now  the  molecules  of  a  magnet  are  as 
truly  separate  from  each  other  as  the  several 
magnets  in  the  series  just  described.  And  it 
is  thought  that  each  molecule  is  a  magnet,  with 
its  north  and  its  south  pole.  Acting  through 
the  minute  distances  that  separate  them,  each 
one  is  polarizing  its  neighbors,  and  hence,  like 
the  series  of  bars,  their  north  poles  must  be  all 
arranged  in  one  direction,  their  south  poles  in  the 
other.  Both  kinds  of  magnetism  act  upon  each  separate 
molecule,  and  keep  it  in  a  magnetic  state.  There  is  no 
transfer  of  the  force  from  one  molecule  to  another  as 
there  is  of  electricity  in  a  charged  body,  so  there  can 
be  no  discharge  of  magnetism.  A  magnet,  like  a  body 
charged  with  electricity,  may  polarize  another,  but  it 
can  not,  like  the  charged  body,  become  neutral  by 
giving  up  its  force.  • 

Why  then  is  the  middle  of  a  magnet  neutral,  while 
only  toward  its  ends  do  the  forces  show  themselves? 
Not  because  the  force  of  one  kind  leaves  the  molecules 
of  one  end  and  gees  to  the  other,  but  because  each 
molecule,  from  one  end  to  the  other,  is  exerting  this 
force  in  the  same  direction.  If  a  row  of  boys  stand  close 
together,  and  all  push  in  the  same  direction,  those  at 


272 


NATURAL     PHILOSOPHY. 


BO  the  molecules  of  a  magnet  near  the 
which  either  force  is  acting,  will 


the  end  of  the  line  will  receive  the  greatest  pressure , 

end  toward 
be  endowed  with  the 
strongest  magnetism.  In  the  middle  of  the  series,  the 
two  forces  are  equal  and  in  opposite  directions,  and 

must  neutralize  each  other. 

TN 

(100.)  If  a  bar  magnet  be  supported  so  as  to  move 
freely  in  a  horizontal  direction,  it  will  rest  only  when 
its  poles  point  north  and  south  or  nearly  so  ;  its  varia- 
tion is  subject  to  both  annual  and  diurnal  changes. 

rig.  132.  1.  If  a  bar  magnet  l)e  supported. 

$ j^  1/L  — A  magnet  may  be  supported  in 

three  ways  so  as  to  have  free 
motion.  It  may  be  balanced  upon 
a  pivot.  (See  Fig.  132.)  It  may  be 
hung  from  a  fixed  support  by  a  fine 
thread  tied  about  its  middle  point, 
rig.  IBS.  (Fig.  133.)  Or  it  may  be,  for  purposes  of 

r        simple  experiment,  fastened  to  a  cork  and 
laid  upon  water. 

2.  It  will  point  north  and  south. — The 
magnet  supported  in  either  of  the  ways 
mentioned,  will  swing  back  and  forth,  un- 
til it  finally  settles  to  rest,  and  it  will  then 
be  found  pointing  north  and  south.  The 
end  which  points  north  is  called  the 
north  pole  :  it  is  evident,  however,  that  its  magnetism 
is  of  the  kind  opposite  to  that  of  the  north  part  of  the 
earth. 

A  slender  bar  magnet  thus  balanced  is  called  a  mag- 
netic needle.  Such  a  needle  is  used  by  mariners  to  di 
rect  them  in  their  long  voyages  across  the  ocean.  ¥01 


a    \    Z 


NATURAL    PHILOSOPHY  273 

this  purpose,  it  is  placed  over  a  card  upon  which  the 
"  points  of  compass,"  north,  south,  east,  west  and  others, 
are  marked,  and  for  protection,  put  into  a  box  hung 
upon  pivots,  so  that  it  will  keep  the  needle  in  a  hori- 
zontal position  amid  all  the  rolling  or  plunging  motions 
of  the  ship.  Such  an  arrangement  is  called  the  mar- 
iner's  com/pass. 

3.  Its  variation. — While  it  is  true  that  the  needle 
points  in  a  direction  which  may  be  described  as 
north  arid  south,  we  must  not  understand  that  this  de- 
scription is  exact.  Indeed  the  needle  seldom  points 
exactly  north  and  south.  There  are  places  at  which  it 
does ;  there  are  others  at  which  it  points  east  of  north  ; 
and  others  at  which  it  points  west  of  the  true  north  and 
south  line.  Its  deviation,  or  in  other  words  what  it 
lacks  of  pointing  in  a  true  north  and  south  line  is 
called  its  variation. 

If  those  places  on  the  earth's  surface  at  which  the 
needle  points  due  north  and  south  be  joined  by  a  line, 
this  line  is  called  the  line  of  no  variation.  This  line 
goes  quite  around  the  globe  in  a  north  and  south  direc- 
tion. It  is,  however,  an  irregular  line,  bending  now  to 
the  eastward  and  then  to  the  westward.  We  may 
trace  its  general  course  through  North  America,  by 
remembering  that  it  strikes  the  continent  near  Cape 
.Lookout,  on  the  coast  of  North  Carolina,  passes  through 
Staunton,  in  Yirginia,  a  little  east  of  Cleveland,  in  Ohio, 
across  Lake  Erie,  and  thence  onward  to  Hudson's  Bay. 

At  places  east  of  this  line  the  variation  is  toward  the 
west ;  at  places  west  of  it  the  variation  is  toward  the 
east. 

4.  The  variation   is  subject  to  annual  and  daily 
changes. — The  variation  of  the  needle  at  any  place  ia 
12* 


274:  NATURAL    PHILOSOPHY. 

continually  changing.  For  example:  the  vaiiation  at 
Washington,  D.  C.,  was  36'  west  in  the  year  1800,  but 
in  1860  it  had  increased  to  2°  54/.  Such  a  change-  is 
going  on  year  by  year  at  all  places.  The  variation 
increases  for  several  years  and  then  again  diminishes* 
So  the  needle  vibrates,  first  westward,  then  eastward, 
and  back  again,  taking  many  years  to  make  a  single 
vibration. 

Besides  this  annual  variation,  the  needle  has  a  daily 
variation,  much  greater  in  summer  than  in  winter — • 
amounting  to  about  15'  in  the  former  and  only  about  10' 
in  the  latter.  At  about  8  A.  M.,  the  north  pole  begins 
to  swing  westward,  and  this  motion  continues  until 
about  1  P.  M.  Soon  after  this  time  it  slowly  moves 
back  toward  the  east  until,  at  about  10  P.  M.,  it  has 
reached  its  starting  point.  It  then  moves  west  again 
until  about  3  A.  M.,  after  which  it  swings  back  to  the 
eastward  until  8  A.  M.  It  completes  these  two  full 
vibrations  every  twenty-four  hours. 

(501.)  If  a  magnetic  needle  be  allowed  to  move 
freely  up  and  down,  it  will  seldom  rest  in  a  horizontal 
position.  Its  inclination  is  called  the  dip  \tf  the  needle. 

In  the  northern  hemisphere  the  north  pole  of  the 
needle  dips ;  in  the  southern  hemisphere  the  south  pole 
dips. 

1.  The  dip  of  the  needle. — If  a  slender  steel  needle 
be  balanced  upon  a  horizontal  axis  so  that  it  may  freely 
move  up  and  down,  and  "be  then  magnetized,  it  will  be 
no  longer  balanced :  the  -north  pole  will  sink  until  the 
needle  takes  a  position  very  much  inclined  (Fig,  134). 
The  amount  of  this  inclination  is  called  the  dip  of  t/it 
needle. 


NATURAL    PHILOSOPHY.  275 

In  the  southern  hemisphere  the  needle  also  takes  an 
inclined  position,  but  there  it  is  the  south  pole  that 
points  downward. 

As  the  dipping  needle  is  carried  farther 
north,  the  dip  increases  until  a  point  is 
reached  where  the  needle  stands  in  a  ver- 
tical position.  Of  course  this  point  must 
be  the  north  magnetic  pole  of  the  earth : 
it  is  a  curious  fact,  that  it  is  not  the  same 
as  the  geographical  north  pole.  It  is  in 
latitude  70°  s5'  N.  and  longtitude  96°  45' 
W. — a  little  north  and  west  of  Hudson's 
Bay.  It  was  found  by  Captain  Ross,  in  the  year  1832. 

Then,  traveling  southward  in  the  southern  hemis- 
phere, the  south  pole  of  the  needle  dips  more  and 
more,  and  there  is  evidently  a  south  magnetic  pole  of 
the  earth.  This  point  has  never  yet  been  found.  (See 
Silliman's  Phys.,  Chap.  III.,  §  1).' 

§    3.    VOf.TAI<«    tCl  ECTKIC1TT. 

(102.)  Yoltaic  electricity  may  be  obtained  by  means 
of  an  apparatus  called  the  voltaic  circuit,  or  better,  by. 
means  of  a  Grove's  or  a  Bunsen's  battery. 

1.  Voltaic  electricity. — We  may  define  voltaic  elec- 
tricity to  be  electricity  which  is  produced  by  chemical 
action.  Let  us  remember  that  the  chemical  properties 
are  those  which  a  body  may  not  show  without  under- 
going some  change  in  its  nature.  So  1jy  chemical 
action,  we  mean  an  action  by  which  some  change  ia 
produced  in  the  nature  of  bodies.  It  will  not  be  for- 
gotten [see  (3.)  ]  that  natural  philosophy  treats  only  of 
the  physical  properties  of  matter,  and  of  phenomena  in 


276 


NATURAL    PHILOSOPHY. 


which  there  is  no  change  in  the  nature  of  bodies.  The 
Btudent  of  natural  philosophy  must  not,  therefore,  ex- 
pect to  find  a  full  explanation  of  the  production  and 
effects  of  voltaic  electricity.  Many  of  its  effects,  how- 
ever, do  belong  to  this  science. 

2.  The    voltaic    circuit. — The    voltaic    circuit,    by 
•which  this  kind  of  electricity  may  be  produced  in  the 
most  simple  way,  is  represented  in  Fig.  135.     Into  a 

Fig.  iss.  glass  vessel  is  put  a  quantity  of  water, 
mixed  with  a  little  sulphuric  acid.  A 
strip  of  copper  and  another  of  zinc  are 
inserted  into  this  liquid,  and  from  the 
upper  ends  of  these  strips  two  metallic 
wires  project.  Now,  when  the  ends 
of  these  two  wires  are  brought  to- 
gether, a  chemical  action  will  take 
place  between  the  water  and  the  zinc, 
by  which  voltaic  electricity  will  be 
produced.  A  multitude  of  little  bub- 
bles of  gas  rising  alongside  of  the  cop- 
per strip  shows  the  action  of  the  elec- 
tric force ;  and  if  the  ends  of  the  wirea 

be  carefully  separated,  a  very  delicate  spark  may  be 

seen  between  them. 

The  ends  of  the  two  wires  are  called  the  poles  of  the 

circuit :  that  from  the  copper  strip  is  the  positive  pole ; 

the  one  from  the  zinc  strip  is  the  negative  pole. 

3.  Grove's  battery. — In  Grove's  battery  we  have  a 
means  of  obtaining  a  more  powerful  action  of  elec- 
tricity than  in  the  simple  circuit,  just  described.     Two 
metals,  zinc  and  platinum,  and  two  liquids,  dilute  sul- 
phuric acid  and  nitric  acid,  are  used.     The  peculiar 
mode  of  putting  these  together  may  be  understood  by 


NATURAL    PHILOSOPHY.  277 

an  attentive  study  of  Fig.  136,  aided  by  the  following 
description : — 

A  glass  vessel  (Y)  is  partly  filled  with  Fi&- 
dilute  sulphuric  acid.  Into  this  fluid  is 
placed  a  zinc  cylinder  (Z)  with  a  slit  from 
top  to  bottom,  to  allow  the  fluid  to  circu- 
late, both  inside  and  outside  of  it,  freely, 
Inside  of  the  zinc  cylinder  is  put  a, porous 
earthenware  cup.  Into  this  cup  is  poured 
strong  nitric  acid,  and  a  strip  of  platinum  is  inserted  in 
this  fluid.  One  wire  being  fastened  to  the  zinc,  and 
another  to  the  platinum,  form  the  poles;  and  when 
brought  together,  and  then  carefully  separated,  a  spark 
of  electricity  may  be  seen. 

The  platinum  pole  is  positive;  the  zinc  pole  is  neg- 
ative. 

4.  Bunserfs  battery. — Bunsen's  battery  differs  from 
the  one  just  described,  by  having  a  carbon  cylinder,  or 
rod,  in  place  of  the  strip  of  platinum.  This  does  not 
greatly  diminish  its  action,  while  it  makes  it  much 
cheaper,  because  platinum  is  a  very  costly  metal. 

(103.)  In  all  these  forms  of  apparatus  the  electricity 
is  produced  by  chemical  action. 

A  part  of  its  force  is  overcome  by  the  resistance  it 
meets  in  going  through  the  poor  conductors  of  the  cir- 
cuit. Its  quantity  and  intensity  depend — the  first  on 
the  size  of  the  metallic  plates  used,  the  second  on  Che 
number  of  plates  employed. 

1.  It  is  produced  ~by  ckemieal  action. — In  the  voltaic 
circuit  a  chemical  action  takes  place  between  the  zinc 
and  the  water.  The  zinc  separates  the  water  into  two 
substances — gases,  called  oxygen  and  hydrogen.  The 


278  NATURAL    PHILOSOPHY. 

hydrogen  escapes:  we  see  it  as  small  bubbles  which 
rise  along  the  side  of  the  copper  plate ;  but  the  oxygen 
combines  with  the  zinc.  By  these  chemical  actions  the 
electric  force  is  produced. 

In  Grove's  and  in  Bunsen's  batteries  there  is  the 
eanie  decomposition  of  water  by  the  zinc;  in  addition 
to  this  the  nitric  acid  is  decomposed.  There  is,  there- 
fore, much  more  chemical  action  than  in  the  simple 
circuit,  and  consequently,  we  should  expect  a  greatei 
electric  force  produced.  For  a  full  explanation  of  these 
chemical  actions  we  must  refer  to  the  science  of  chem- 
istry. 

2.  TJt.e  resistance  it  meets. — The  difference  between 
conductors  and  non-conductors  of  electricity ,  has  already 
been  given.  We  must  now  attend  to  the  fact  that  no 
substance  is  a  perfect  conductor.  Even  silver  ani 
copper  wires,  which  are  among  the  very  best  con- 
ductors, do  not  allow  electricity  to  pass  through  them 
with  perfect  freedom ;  they  resist  its  action  at  every 
point.  So,  too,  the  materials  of  which  the  batteries  are 
composed,  being  imperfect  conductors,  resist  the  action 
v  of  the  force  at  every  point,  in  the  fluid,  in  the  plates 
of  metal,  and  in  the  wires  which  join  them. 

The  resistance  which  a  wire  offers  to  the  action  of 
electricity  through  it,  depends  upon  the  material  of 
which  it  is  made,  and  upon  its  size.  The  metals  are 
the  best  conductors,  silver  standing  at  the  head  of  the 
list,  copper  next,  and  lead  being  among  the  poorest. 
The  larger  the  wire,  the  less  resistance  it  offers. 

The  electric  force  evolved  by  the  chemical  action  ir 
the  battery  must,  therefore,  exert  itself  first  to  overcome 
the  resistance  it  meets,  and  the  force  not  thus  expended 
may  be  used  for  other  purposes. 


NATURAL    PHILOSOPHY.  279 

3.  Its  quantity  and  intensity. — If  large   plates   of 
metal  are  used  in  the  battery,  so  that  the  surface,  on 
which  the  chemical  action  takes  place,  is  greater,  the 
quantity  of  electricity  evolved  will  be  increased,  and 
yet  it  will  be  found  no  better  able  to  overcome  resist- 
ance than  before.     If,  for  example,  a  single  Grove's 
battery  of  common  size,  will  give  electricity  which  will 
go,  as  a  spark,  through  a  layer  of  air  -^  of  an  inch 
between  the  poles,  it  will  be  found  that  another  cell, 
with  plates  of  metal  four  times  as  large,  will  not  give  a 
spark  any  longer  than  -^  of  an  inch. 

The  power  of  electricity  to  overcome  resistance,  is 
called  its  intensity.  It  does  not  depend  upon  its 
quantity.  There  may  be  a  great  quantity  of  electricity 
with  very  little  intensity,  or  there  may,  on  the  other 
hand,  be  a  very  small  quantity  with  great  intensity. 
We  are  familiar  with  something  analogous  to  this  in 
heat,  and  it  may  help  us  in  getting  a  clearer  idea  of 
the  difference  between  quantity  and  intensity.  In  a 
burning  match  there  is  a  small  quantity  of  heat,  but  it 
is  very  intense ;  while  in  a  large  cask  of  warm  water 
there  is  a  great  quantity  of  heat,  with  very  little^inten- 
sity. 

4.  Quantity  depends  upon  size  of  plates. — By  in- 
creasing the  size  of  metallic  surfaces  in  any  circuit,  the 
quantity  of  electricity  is  increased.     This  may  be  done 
in  two  ways:  1st,  by  having  a  single  plate  of  each 
metal  made  large ;  or,  2d,  by  having  several  small  ones 
of  each  kind  joined  together.     The  last  mode  is  the 
one  usually  employed.     If  in  several  cells  of  Grove's 
battery  all  the  platinum  strips  are  joined,  they  will  be 
equivalent  to  one  large  platinum  surface.     If  all  the 
tine  cylinders  be  joined  together  they  form  one  large 


280  NATURAL    PHILOSOPHY. 

surface  of  ziiic.  If,  then,  a  wire  from  the  platinum  be 
brought  iu  contact  with  another  from  the  zinc,  the 
circuit  will  be  completed,  and  a  battery  for  quantity 
will  be  formed. 

5.  Intensity  depends  upon  the  number  of  plates.- - 
But  if  several  cells  of  the  battery  are  joined  by  con- 
necting the  platinum  of  one  cell  with  the  zinc  of  the 
next ;  the  platinum  of  this  with  the  zinc  of  the  next, 
and  so  on,  finally  joining  the  platinum  of  the  last  with 
the  zinc  of  the  first,  the  intensity  of  the  electricity  will 
be  vastly  increased. 

When  the  resistance  to  be  overcome  is  considerable, 
an  intensity  battery  will  be  used  ;  in  most  other  cases 
the  quantity  battery  is  employed.  (See  Silliman'a 
Physics,  p.  581.) 

The  greatest  difference  between  voltaic  electricity  and 
frictional  electricity  is  this:  voltaic  electricity  is  re- 
markable for  its  great  quantity  but  feeble  intensity ', 
while  frictional  electricity  is  equally  remarkable  for  ita 
great  intensity  but  small  quantity. 

(104.)  Among  the  mechanical  effects  of  voltaic  elec- 
tricity, we  notice  heat,  light,  magnetism,  and  induction. 

Electricity  produces  heat  whenever  it  is  resisted  in 
its  action.  It  makes  the  most  intense  light  by  passing 
through  air  between  two  charcoal  points.  It  produces 
magnetism  by  acting  through  a  wire  which  encircles  a 
bar  of  iron.  Upon  this  principle  the  electric  telegraph 
and  other  useful  instruments  are  made.  By  changing 
the  direction  of  the  force  around  the  bar,  the  poles  of 
the  magnet  are  reversed.  One  conductor  of  electricity 
induces  electricity  in  another  near  it. 

I.  Heat.  —  Electricity,  when  resisted  in  its  action, 


NATURAL    PHILOSOPHY.  281 

§hows  itself  as  heat.  When  it  acts  through  a  fine  wire, 
the  wire  may  be  made  red-hot,  and  in  many  cases 
melted,  by  the  heat  produced.  Several  inches  of  fine 
iron  wire  may  be  thus  melted  by  a  battery  of  12  or 
15  cells.  This  power  of  electricity  is  applied  to  the 
exploding  of  gunpowder,  for  blasting  rocks.  For  this 
purpose,  a  cartridge  is  made  by  filling  a  tin  tube  with 
gunpowder,  and  corking  its  ends  tightly.  Through  one 
of  the  corks  two  copper  wires  pass,  joined  in  the  pow- 
der by  a  fine  steel  wire  soldered  to  their  ends.  The 
copper  wires  are  then  connected  with  the  poles  of  a 
distant  battery.  The  instant  that  the  circuit  is  made, 
the  fine  wire  in  the  gunpowder  is  melted,  and  its  heat 
explodes  the  gunpowder. 

No  other  artificial  heat  can  be  made  so  intense  as 
that  produced  by  electricity.  But  since  it  is  associated 
with  intense  light,  we  will  notice  it  in  that  connection. 

2.  Light. — When  the  wires  which  lead  from  the  poles 
of  a  powerful  battery  are  tipped  with  charcoal  points, 
if  these  points  are  brought  in  contact  and  then  sepa- 
rated for  a  short  distance,  the  space  between  them  will 
be  bridged  over  by  an  arch  of  blinding  light.  On  ex- 
amination, this  light  is  found  to  be  due  to  the  intense 
whiteness  of  the  carbon  tips,  chiefly,  but  not  to  their 
combustion  at.  all,  since,  in  a  vacuum,  where  combus- 
tion can  not  occur,  the  light  is  of  equal  intensity. 

The  electric  light  is  unsteady ;  for  this  reason,  and 
because  of  its  unpleasant  brilliancy,  it  has  not  been  suc- 
cessfully usedfor  lighting  streets  and  public  places.  It  has 
been  used,  however,  with  excellent  effect  in  light-houses. 

The  heat  of  this  arch  of  light  is  wonderfully  intense. 
Platinum,  more  difficult  to  melt  than  other  metals, 
melts  in  this  heat  like  wax  in  the  flame  of  a  taper. 


NATURAL    PHILOSOPH5T. 


Fig.  187. 


Even  quartz,  and  other  bodies  equally  difficult  to  melt, 
are  fused  bj  it  readily. 

3.  Magnetism. — Bars  of  soft  iron  inclosed  in  coils  of 
wire  are  called  electro-magnets.  The  coil  is  generally 
called  a  helix.  If  the  two  ends  of  the  coil  be  fastened 
to  the  poles  of  a  battery,  the  electricity  darts  instantly 
through  the  coil,  and  the  iron  becomes  a  magnet.  The 
bar  of  iron  may  be  of  any  form  ;  when  in  the  shape  of 
the  horseshoe  magnet,  the  coil  is  made  in  two  parts,  one 
encircling  each  arm  of  the  iron.  A  horseshoe  electro- 
magnet A  B,  is  seen  in  Fig.  137. 

The  strength  of  elec- 
tro-magnets is  something 
surprising.  One  belong- 
ing to  Yale  College, 
weighing  591bs,  lifted  a 
weight  of  2,500  Ibs.  (See 
Silliman's  Phys.,  p.  610.) 
This  wonderful  power  is 
developed  only  when  a 
bar  of  soft  iron,  the  ar- 
mature, C  D  (Fig.  137), 
is  in  contact  with  the 
poles.  "Without  this,  the 
magnet  will  not  lift  a 
tenth  part  of  what  it 
could  otherwise  sustain. 
The  iron  is  magnetic 
|  only  while  the  electric- 
ity acts  around  it:  let 
the  circuit  be  in  any 
way  broken,  and  the  grasp  of  the  giant  is  at  once  loosed : 
the  load  falls.  On  again  making  the  circuit,  the  mag 


NATURAL    PHILOSOPHY. 


283 


net  i  instantly  as  strong  as  before.  The  rapidity  with 
whicL  an  iron  bar  will  thus  receive  and  part  with  ita 
magnetism,  as  the  circuit  is  made  and  broken,  is  truly 
astonishing.  By  the  electric  register  for  vibrations  [see 
(46.)  3],  the  author  has  caused  an  electro-magnet  to  un- 
dergo this  change  at  the  rate  of  8,400  times  a  minute. 

4.  The  electric  telegraph  acts  on  this  principle. — It  is 
upon  this  principle  that  the  electric  telegraph  has  ena- 
bled man  to  send  his  thoughts,  with  lightning-speed, 
across  continents,  and  under  oceans,  to  his  most  distant 
fellow-men. 

Having  found  that  a  bar  of  iron  will  become  magnet- 
ic as  often  as  electricity  is  sent  round  it,  and  cease  to  be 
so  on  the  instant  the  force  stops,  let  us  next  notice  that 
the  wires  conveying  the  force  may  be  of  any  length, 
even  miles,  and  hence  the  battery  may  be  in  one  city, 
while  the  magnet  may  be  in  another,  and  still  an  arma- 
ture will  be  drawn  against  its  poles  every  time  the  cir- 
cuit is  made.  Now,  if  the  motion  of  an  armature  to 
and  from  the  poles  can  be  made  to  write,  then  can  mes- 
sages be  sent  from  one  city  to  another. 

The  apparatus  consists  of  three  parts :  the  key,  the 
line,  and  the  register. 

The  key  is  an  instrument  by  which  the  circuit  can  be 
made  and  broken  at  will.  It  is  in  the  office  from  which 
the  message  is  to  be  sent.  A  brass  lever,  L(Fig.  138), 
moves  on  an  axis,  A. 
Two  projection^  n  and 
m,  from  its  lower  side, 
are  just  above  two  oth- 
ers, one  of  which  (a)  is 
joined  by  a  wire  with 
the  battery,  while  from 


18S- 


284 


NATURAL     PHILOSOPHY. 


the  axis  A,  another  wire  reaches  to  the  distant  station. 
By  pressing  the  finger  on  the  end  of  this  lever,  the  point 
is  brought  in'contact  with  the  battery  wire  at  a,  and  the 
electricity  can  then  act  through  the  lever,  from  the  bat- 
tery wire  to  the  wire  from  the  axis.  Let  the  finger  be 
lifted,  and  the  lever  will  rise  by  the  action  of  a  spring, 
s,  and  the  circuit  is  broken. 

The  line  consists  of  a  wire  (L)  reaching  from  the  key 
over  the  country  to  distant  places.  Formerly  two  wires 
were  used,  one  from  the  positive  pole,  the  other  from 
the  negative  pole  of  the  battery ;  but  it  has  been  found 
that  the  earth  may  take  the  place  of  one  of  these  wires. 

The  register  is  shown  in  Fig.  139.     One  of  the  screw 

Fig.  139. 


cups  at  the  end  of  the  instrument  is  connected  with  the 
line  wire  L,  from  the  key  of  the  distant  station,  while 
the  other  M,  is  connected  with  the  earth.  When  the 
circuit  is  made,  the  electric  force  darts  around  the  elec- 


NATURAL    PHILOSOPHY.  285 

tro-magnet,  and  draws  the  armature  down  against  ita 
poles  :  this  raises  the  long  arm  of  the  lever,  and  presses 
the  steel  point  I,  against  a  strip  of  paper,  which  ia 
pulled  along  from  the  spool  E,  by  clock-work.  When 
the  circuit  is  broken,  the  armature  is  released  from  the 
poles  of  the  electro-magnet ;  the  long  arm  of  the  lever 
falls  by  its  own  weight,  or  by  the  force  of  a  spring,  and 
the  point  is  removed  from  the  paper. 

If  the  point  press  the  paper  for  an  instant  only,  a  dot 
will  be  made,  but  if  it  be  held  against  it  for  a  longer 
time,  a  dash  will  be  left  upon  it.  Now,  the  letters  of 
the  alphabet  are  represented  by  dots  and  dashes.  Two 
operators  who  know  this  alphabet,  can  communicate 
with  each  other;  one  by  pressing  the  key  causes  a  seriea 
of  dots  and  dashes,  to  be  marked  upon  the  paper  of  the 
register  at  a  distant  place,  while  the  other  can  read 
this  written  language. 

Such"  is  an  outline  of  the  essential  parts  of  the  electric 
telegraph  (see  Silliman's  Phys.,  p.  616),  the  greatest 
triumph  of  modern  science. 

The  steam-engine  and  the  electric  telegraph  may  be 
regarded  as  the  body  and  the  spirit  of  modern  civiliza- 
tion, the  first  distributing  matter ,  the  second  thought; 
both  laboring  toward  a  more  general  diffusion  of  com- 
fort and  knowledge  and  sympathy  among  men. 

5.  The  poles  are  reversed  by  changing  the  direction 
of  the  force. — Every  electro-magnet  has  a  north  and  a 
south  pole,  but  they  may  be  made  to  change  from  end 
to  end  instantly,  by  changing  the  direction  of  the  elec- 
tricity in  its  passage  round  the  bar.  We  know  that  the 
electricity  from  Grove's  battery  always  acts  from  the 
platinum  through  the  wires  to  the  zinc  :  it  will  enter  a 
coil  by  the  wire  which  comes  from  the  platinum  ;  it 


286  NATURAL    PHILOSOPHY. 

will  leave  the  coil  by  that  which  goes  to  the  zinc.  By 
this  means  it  is  easy  to  trace  the  diiection  of  the  force 
through  the  coil.  Notice  again,  that  when  the  ends  of 
the  coil-wire  are  made  to  change  places  at  the  poles  of 
the  battery,  the  direction  of  the  force  around  the  coil  ia 
reversed :  if  it  were  going  around  in  the  same  direction 
that  the  hands  of  a  clock  travel  around  the  dial,  it  will, 
on  changing  the  poles,  instantly  go  in  the  direction 
which  the  hand  goes  when  the  clock  is  being  set  back. 
If  these  two  points  are  understood,  we  may  give  the 
following  law  : — The  south  pole  of  the  electro-magnet 
will  be  at  that  end  of  the  coil  where  the  electricity  en- 
ters, when  the  force  acts  around  the  coil  in  the  same 
direction  which  the  hands  of  a  clock  move  over  the 
dial. 

6.  One  conductor  induces  electricity  in  anoiky. — 
That  a  wire  through  which  electricity  is  acting  excites 
electricity  in  another  one  near  it,  was  proved  by  Fara- 
day in  the  following  way.  Two  very  long,  silk  covered, 
copper  wires  were  wound  into  a  coil,  so  that  they 
should  run  side  by  side  throughout  their  entire  length, 
but  yet  be  perfectly  insulated  from  each  other.  When 
the  two  ends  of  one  of  these  wires  were  connected  with 
a  battery,  while  the  two  ends  of  the  other  were  con- 
nected with  a  galvanometer — an  instrument  for  detect- 
ing the  presence  of  voltaic  electricity,  the  galvanometer 
announced  the  action  of  the  force  in  the  mre  which 
had  no  connection  whatever  with  the  battery.  The 
direction  of  this  action  is  the  same  as  in  the  battery 
current.  When  the  circuit  of  the  battery  was  broken, 
the  galvanometer  announced  a  current  in  the  other  wire 
going  in  the  opposite  direction. 

These  currents  are  called  secondary  or  induced  cur 


NATURAL    PHILOSOPHY.  287 

rents ;  they  are  but  momentary,  but  are  renewed  at 
every  interruption  of  the  battery  circuit. 

If  a  bar  of  soft  iron  be  thrust  into  the  helix,  the 
force  of  the  induced  current  is  greatly  intensified. 

It  is  upon  this  principle  of  induction  that  the  Rlmmi- 
korf  Coils  are  constructed  (see  Silliman'sPhys.,  p.  627). 
In  these  important  instruments  there  is  first  a  coil  ot 
large  copper  wire,  inside  of  which  is  put  a  bundle  of 
iron  wires.  Outside  of  this,  called  the  primary  coil,  is 
placed  another,  called  the  secondary  coil,  made  of  fine 
copper  wire,  from  10,000  to  80,000  feet  in  length.  The 
two  coils  are  insulated  from  each  other  with  the  utmost 
care.  The  ends  of  the  primary  coil  are  attached  to  the 
battery,  while  from  the  ends  of  the  secondary  coil  the 
electricity  is  taken  in  experiments. 

The  effects  produced  by  this  apparatus  are  beyond 
comparison  more  intense  than  from  a  battery  alone,  or 
an  electrical  machine.  "When  the  battery  circuit  is 
rapidly  made  and  broken,  a  torrent  of  brilliant  sparks 
leap  from  one  end  of  the  secondary  coil  to  the  other — in 
one  of  the  American  instruments,  a  distance  of  sixteen 
inches.  The  shocks  caused  by  it  are  dangerous,  in  a 
degree  approaching  those  of  the  lightning  stroke.  The 
heat  produced  is  very  intense,  while  the  light  obtained 
by  passing  its  electricity  through  rarefied  air,  or  through 
various  gases,  is  beautiful  beyon  I  description. 


2J»8  NATURAL    PHILOSOPHY. 


CONCLUSION. 


(105.)  WE  have  now  become  acquainted  with  the 
important  first  principles  of  natural  philosophy.  OUT 
attention  has  been  given  exclusively  to  those  truths 
which,  because  of  their  importance  in  the  theories  of 
science,  or  because  of  their  practical  applications  to  the 
wants  of  life,  are  essential  to  be  known  by  those  who 
would  be  prepared  for  the  higher  advantages  of  the 
college,  and  equally  necessary  to  those  who  expect  to 
become  intelligent  members  of  society  without  the 
higher  courses. 

We  first  learned  that  the  study  of  natural  philosophy, 
in  distinction  from  chemistry,  describes,  and  attempts  to 
explain,  all  those  phenomena  in  which  there  is  no 
change  in  the  nature  of  bodies. 

We  then  found  that  the  words  molecule,  inertia, 
attraction,  and  repulsion,  express  the  four  fundamental 
thoughts  which  open  the  way  to  an  explanation  of  all 
the  phenomena  of  which  the  science  treats. 

In  the  application  of  these  thoughts  we  noticed  first, 
that  attraction  and  repulsion,  acting  on  the  molecules 
of  matter,  produce  the  three  physical  forms,  solid,  liquid 
and  gaseous,  and  we  were  then  able  to  describe  the 
^huracteristic  properties  of  these  groups  of  bodies. 

Second. — That  attraction  and  repulsion,  acting  upon 
masses,  cause  the  phenomena  of  rest  and  motion  :  and 
this  introduced  us  to  the  explanation  of  the  laws  which 


NATURAL    PHILOSOPHY.  289 

control  the  wonderful  variety  of  motions  in  nature  and 
the  important  action  of  machines. 

Third. — That  attraction,  repulsion,  and  inertia,  act- 
ing upon  the  masses  or  molecules  produce  vibrations, 
and  we  were  able  to  obtain  laws  for  this  peculiar  kind 
of  motion.  And  when  we  noticed,  further,  that  the 
vibrations  of  molecules  affect  our  senses,  we  had  found 
the  key  to  unlock  the  gates  which  opened  into  the  fields 
of  sound,  of  light,  and  of  heat,  and  were  then  able  to  ex- 
plain their  wonderful  effects. 

Fourth. — That  the  constantly  opposite  action,  or 
struggle,  of  attraction  and  repulsion  among  the  mole- 
cules of-bodies  shows  itself  as  electricity,  and,  following 
this  thought,  we  became  acquainted  with  the  curious 
effects  of  electrical  action. 

Nor  are  the  applications  of  the  four  fundamental 
thoughts  limited  to  the  phenomena  which  have  been 
presented  in  the  compact  outline  of  the  science  just 
completed.  The  most  extended  commentary — one 
which  should  give  all  the  explanations  of  those  phe- 
nomena in  which  there  is  no  change  in  the  nature  of 
bodies — if  written,  would  only  Jill  up  the  scheme  which 
these  four  thoughts  suggest.  Indeed,  they  seem  to  be 
the  frame- work  upon  which  the  fabric  of  material  things 
has  been  built. 

One  who  has  never  given  special  attention  to  the 
study  of  nature,  finds  his  mind  overwhelmed  by  the 
great  diversity  of  material  objects  which  the  world  pre- 
sents, and  he  beholds  them  with  amazement,  or  it  may 
be  with  indifference  ;  but,  in  the  light  of  careful  obser- 
vation and  analysis,  the  system  of  material  things  is 
simple  and  orderly,  displaying  the  infinite  knowledge, 
power,  and  skill  of  a  Divine  Architect. 

13 


290  NATURAL    PHILOSOPHY. 


APPENDIX. 


I. 

(CHAPTER  V.   CONTINUED). 
§.    4.    MUSICAL   AND   SENSITIVE   FLAMES. 

(106.*  WHEN  a  gas  flame  burns  within  a  glass  tuba 
a  musical  sound  is  produced.  The  pitch  of  the  tone 
depends  on  the  length  of  the  tube  and  the  size  of  the 
flame.  A  silent  flame  may  be  made  to  sing  by  sound- 
ing near  it,  the  note  of  the  tube.  Naked  flames  are 
also  sensitive  to  the  action  of  neighboring  sounds. 

1.  The  musical  flame.  —  Let  a  flame  of  common  coal 
gas,  placed  under  the  end  of  a  glass  tube  T  (Fig.  140), 
be  slowly  raised  into  it  ;  when  a  particular  height  is 
reached,  the  flame,  if  small  enough,  will  burst  forth  in- 
to a  loud  and  continuous  sound.  This  sound  is  often 
harsh,  sometimes  melodious.  At  the  beginning  it  is 
sometimes  low  and  smooth,  like  the  whistle  of  a  very 
distant  locomotive,  but  as  the  experiment  goes  on,  the 
intensity  of  the  sound  rapidly  increases  until,  like  the 
long  monotonous  screech  of  the  engine  at  hand,  it 
becomes  almost  unbearable. 

In  tubes  of  tin  and  pasteboard,  sounds  of  different 
quality  are  obtained. 

That  a  gas  flame  flutters  when  exposed  to  a  gentle 


NATURAL.  PHILOSOPHY. 


291 


breoze,  is  a  fact  sufficiently  familiar.  Now,  this  flut- 
tering flame,  like  a  vibrating  tongue  or  reed,  must 
cause  vibrations  in  Fig.  uo. 

the  air  around  it. 
Here  is  the  key  to 
the  explanation  of 
musical  flames. 

The  air  in  the 
tube  is  heated  by 
the  flame ;  it  rises : 
an  upward  current 
through  the  tube  is 
thus  produced ;  the 
flame  flutters  in 
this  current,  and 
causes  a  system  of 
waves,  whose  rapid- 
ity and  amplitude 
give  pitch  and  in- 
tensity to  the  note 
produced.  If  we 
inquire  further 
about  the  cause  of 
the  fluttering,  we 
are  told  that  experi- 
ments by  Faraday  proved  that  gas  issues  from  a  burn- 
er in  an  unsteady  stream,  due  to  the  friction  against 
the  sides  of  the  tube,  and  that  in  burning,  it  makes  a 
series  of  inaudible  explosions.  A  current  of  air  height- 
ens both  of  these  effects,  and  makes  them  sensible. 

That  a  musical  flame  is  thus  intermittent  is  shown  by 
the  following  beautiful  experiment.  The  tube  T  (Fig. 
141),  io  blackened  so  as  to  keep  the  light  from  falling 


292 


NATURAL    PHILOSOPHY. 


on  the  Bcreen  placed  behind  it  at  S.    A  concave  mir 
ror  M,  in  front  of  the  flame,  forms  an  inverted  image 
of  it  on  the  screen.    If  the  mirror  is  turned  horizontally, 

Fig/141. 


while  the  flame  is  silent  and  steady,  the  image  wiD 
move,  and  if  the  motion  of  the  mirror  is  swift,  an  un- 
broken band  of  light  will  be  seen  on  the  screen.  But, 


NATURAL    PHILOSOPHY.  393 

if  when  the  flame  is  singing,  the  mirror  is  swiftly  turned, 
a  series  of  distinct  images  will  appear. 

This  experiment  teaches,  that  in  the  act  of  singing, 
the  light  of  the  flame  is  quenched  at  intervals.  And 
if,  as  Dr.  Tyndall  supposes,  the  spaces  between  the  im- 
ages are  absolutely  dark,  then  the  flame  must  be 
entirely  put  out  at  intervals,  the  heat  being  sufficient 
to  instantly  relight  it. 

2.  The  pitch  of  the  note. — In  these  tubes,  as  in  organ 
pipes,  the  pitch  of  the  sound  depends  upon  the  length  of 
the  tube.     But  while  the  pitch  depends  chiefly  upon 
the  length  of  the  tube,  it  is  partly  governed  by  the  sizo 
of  the  flame.     If  one  tube  is  just  twice  the  length  of 
another,  its  fundamental  note  is  an  octave  below,  but 
when  placed  over  a  flame  whose  size  fits  it  to  sing  in 
the  shorter  tube,  the  note  of  the  shorter  tube  will  be 
produced.     Then  let  the  flame  be  gradually  enlarged 
and  in  a  little  time,  the  low  fundamental  note  of  the 
tube  suddenly  bursts  forth.     By  varying  the  size  of  the 
flame  it  is  possible  to  obtain  the  fundamental  note,  its 
octave,  and  its  four  harmonics  from  the  same  tube. 

3.  A  silent  flame  responds  to  a  sound. — At  one  place 
in  the  tube  a  flame  spontaneously  bursts  into  sound ;  at 
the  other,  near  the  end,  it  trembles,  but  does  not  sing. 
Now,  between  these,  there  is  a  third  place,  at  which  the 
flame  is  silent,  but  where,  if  the  proper  note  is  sounded, 
"  it  stretches  forth  its  little  tongue  and  begins  its  song." 
Dr.  Tyndall  goes  on :  I  stop  the  music  ;  and  now  stand- 
ing as  far  from  the  flame  as  the  room  will  allow  me, 
I  command  the  flame  to  sing.     It  obeys  immediately. 
A  pitch,  pipe  or  any  other  instrument  which  yielda  a 
note  of  proper  pitch,  produces  the  same  effect. 

4-.  Sensitive  flames. — The  name  "sensitive  flames'"  ia 


204  NATURAL    PHILOSOPHY. 

given  to  those  which,  without  being  inclosed  in  tubes 
are  affected  by  sounds.  Certain  sounds  in  an  instru- 
mental concert  cause  curious  motions,  often,  of  the  gas 

77  e> 

flames  in  the  room.  This  observation  was  first  pub- 
lished in  1858.  The  motions  referred  to  consist  of  a 
"  jumping  "  of  the  flame  to  considerable  height,  or  a 
thrusting  forth  of  tongues  of  flame  from  its  upper  edge. 
(See  Tyndall,  On  Sound  p.  230.) 

An  effect  just  opposite  this,  the  shortening  of  tall 
flames,  was  first  noticed  by  Mr.  Barrett  of  London,  in 
1865.  He  says  (Chem.  News,  Amer.  Rep.,  July, 
1868)  : — "A  jet  of  gas  issuing  from  a  Y-shaped  orifice 
was  found  to  be  quite  insensible  to  sound  until  the 
flame  reached  a  height  of  10  or  12  inches  (see  Fig. 
142),  and  then,  at  the  sound  of  certain  high  notes,  the 
flame  shortened  and  spread  out  into  a  fan  shape." 
Another  flame  he  thus  describes : — "  So  sensitive  is  this 
flame  that  even  a  chirp  made  at  the  far  end  of  the  room 
brings  it  down  more  than  a  foot.  Like  a  living  be- 
ing, the  flame  trembles  and  cowers  down  at  a  hiss — it 
crouches  and  shivers  as  if  in  agony  at  the  crisping  of 
this  metal  foil,  though  the  sound  is  so  faint  as  scarcely 
to  be  heard.  It  dances  in  tune  to  the  waltz  played  by 
this  musical  box — and,  finally,  it  beats  time  to  the 
ticking  of  my  watch." 

Mr.  Barrett  also  suggests  that  these  flames  may  yet 
be  turned  to  some  use,  and  to  illustrate,  suggests  an 
arrangement  shown  in  Fig.  142. 

Near  the  taL  sensitive  flame  a,  stands  two  vertical 
brass  rods,  5  c.  Projecting  from  these  rods  are  two 
metallic  ribbons,  made  of  layers  of  silver,  gold,  and 
platinum  welded  together.  The  ends  of  the  ribbons 
are  about  half  an  inch  apart.  By  heat  the  different 


NATURAL    PHILOSOPHY. 


295 


metals  expand  unequally,  and,  bending  the  ribbons, 
bring  their  ends  together.  The  brass  rods  are  connected 
by  wires  with  an  electric  bell  at  a  distance. 

Now,  as  long  as  the  tall  flame  Fig.  us. 

is  not  disturbed,  the  metallic  rib- 
bons are  not  in  contact:  the  cir- 
cuit is  broken,  and  the  bell  is 
silent ;  but  at  the  sound  of  a  whis- 
tle the  flame  jumps  down,  warms 
the  ribbons,  completes  the  electric 
circuit,  and  rings  the  distant  bell. 
A  flame,  sensitive  to  the  sound  of 
burglars'  tools,  might  in  this  way 
sound  an  alarm. 

Another  quotation  from  the 
same  lecturer  may  end  this  sub- 
ject. "  Imagine  that  when  en- 
chanted by  the  performance  of 
some  well  executed  opera  or  ora- 
torio, a  companion  by  our  side  were  to  say — c  Well,  after 
all,  of  what  good  are  these  fine  sounds  ?  to  what  practical 
end  can  you  turn  this  music  V  Should  we  not  instantly 
condemn  a  speech  so  characteristic  of  a  sordid  and 
sensuous  mind  ?  And  when  the  student  of  nature  is 
listening  with  admiration,  and  even  awe,  to  the  sweet 
though  silent  music  sung  to  him  by  every  object  of  his 
diligent  study — by  air  and  water,  by  flowers  and  flames, 
he  is  conscious  that  he  bows  before  an  oratorio  as  far 
above  that  of  Handel,  as  the  works  of  the  Creator  are 
superior  to  the  compositions  of  the  creature." 

§  5.  METHODS   OF   REGISTERING   VIBRATIONS. 

(107.)  Yarious  methods  have  been  devised  for  regia- 


296  NATURAL    PHILOSOPHY. 

tering  vibrations.  The  syren  shows  the  number  of  air 
puffs  corresponding  to  the  sound  it  makes.  Savart'a 
wheel  tells  the  number  of  taps  of  a  solid  body  to  pro- 
duce a  continuous  sound  of  any  pitch.  In  Duhamel's 
graphic  method,  the  vibrating  solid  traces  a  sinuouo 
line :  in  Scott's  phonautograph  this  method  is  applied 
to  all  sonorous  vibrations.  By  the  author's  electric 
register,  vibrations  whose  amplitude  are  appreciable, 
either  in  solids  or  liquids,  may  be  directly  registered. 

1.  Registering  vibrations. — Sound,  light,  heat,  and 
perhaps  electricity,  are  caused  by  vibrations.    The  study 
of  these  subjects,  then,  whenever  we  pass  beyond  the 
mere  description  of  sensible  phenomena,  is  the  study  of 
the  nature  and  laws  of  vibrations.     The  nature  of  the 
vibrations  which  produce  heat  and  light,  can  only  be 
inferred  from  the  phenomena  they  cause.     Almost  in- 
conceivably rapid,  they  can  be   neither  counted  nor 
measured   by   any   direct    experiment.     What    agent 
Bwifter  than  they,  able  to  magnify  their  amplitude  and 
mark  their  number !     Electricity  is  swifter  than  light : 
will  the  future  develop  some  means  by  which  it  may 
keep  pace  with,  and  mark  the  ebb  and  flow  of  luminous 
waves?     The  boldest  experimenter  would  yet  hardly 
dare  venture  the  conjecture. 

Sound  waves  have,  however,  been  registered  by  direct 
experiment. 

2.  The  syren. — This  instrument,  already  described 
[See  (56.)],  registers  the  number  of  air  puffs  by  which 
its  sound  of  any  pitch  is  made,  and  the  number  of  puffs 
is  taken  as  the  number  of  vibrations.     Improved  forma 
of  this  beautiful  and  accurate  instrument  are  described 
in  Tyndall's  Lectures  "  On  Sound." 

3.  Savart^s  wheel. — In   this    instrument   a  toothed 


NATURAL    PHILOSOPHY.  397 

wheel  is  turned  by  another  -wheel  and  band.  A  thin 
metallic  tongue  is  so  placed  that  the  end  of  it  presses 
gently  against  the  teeth  of  the  wheel.  When  the  wheel 
turns,  this  tongue  taps  against  every  tooth,  and  when 
turned  fast  enough,  these  taps  are  linked  together  into 
a  continuous  sound.  An  index,  attached  to  the  axis  of 
the  toothed  wheel,  shows  the  number  of  taps,  and  the 
number  of  taps  corresponding  to  any  sound  is  taken  as 
the  number  of  vibrations  to  produce  it. 

On  the  principle  that  sounds  of  the  same  pitch  are 
made  by  vibrations  of  the  same  rapidity,  both  the  syren 
and  Savart's  wheel  may  indirectly  register  the  number 
of  vibrations  made  by  any  sounding  body.  Pitch  either 
of  these  instruments  in  unison  with  the  sound  of  the 
piano,  for  example,  and  its  dial  tells  the  number  of 
vibrations  made  by  the  wire.  Owing  to  the  difficulty 
of  judging  an  exact  unison,  and  to  the  greater  difficulty 
of  keeping  a  perfectly  uniform  motion  of  the  instru- 
ments, a  direct  registry  would  seem  to  be  more  satis- 
factory. 

4.  The  graphic  method. — The  graphic  method  of 
Duhamel  consists  in  fixing  a  fine  metallic  point  to  the 
body  emitting  the  sound,  and  causing  it  to  trace  the 
vibrations  on  a  properly  prepared  surface. 

The  apparatus  consists  of  a  cylinder,  around  which 
is  rolled  a  sheet  of  paper  covered  with  a  thin  film  of 
lamp-black.  Suppose  the  vibrations  of  a  tuning  fork 
are  to  be  registered.  The  handle  of  the  fork  is  set  in 
a  vise,  or  other  firm  support :  a  fine  point  is  cemented 
to  one  of  its  prongs,  and  the  cylinder  is  then  BO  placed 
that  the  point  will  gently  rest  upon  its  surface.  Now, 
if  the  cylinder  is  turned,  the  point  will  trace  a  straight 
line,  by  scraping  off  the  black  film  in  its  path  over  the 

13* 


298  NATURAL    PHILOSOPHY. 

white  paper;  but  when  the  fork  vibrates,  the  point 
moves  with  it,  and  instead  of  a  straight  line,  it  traces 
a  sinuous  path,  each  undulation  representing  a  double 
vibration.  By  counting  the  number  of  undulations 
made  in  given  time,  the  number  of  vibrations  is  known. 
(Atkinson's  Ganot's  Phys.,  p.  159.) 

5.  The  phonautograph. — M.  Leon  Scott  has  applied 
his  graphic  method  to  all  sonorous  vibrations  whatever. 
His  apparatus,  called  the  phonautograph,  consists  of  a 
box  about  a  foot  and  a  half  long,  and  one  foot  in  its 
greatest  diameter,  having  the  shape  of  a  barrel  or  cask. 
It  is  made  of  plaster  of  Paris,  one  end  being  open,  the 
other  closed  by  a  solid  head,  to  the  middle  of  which  is 
fitted  a  copper  tube  having  a  thin  membrane  stretched 
over  its  outer  end.     Near  the  center  of  this  membrane 
is  fixed  a  very  light  projecting  point,  in  front  of  which 
turns  the  cylinder  covered  with  blackened  paper,  the 
same  as  in  DuhamePs  method. 

Now,  whenever  a  sound  is  made  in  front  of  the  cask, 
the  air  in  it,  the  membrane,  and  its  projecting  point, 
will  vibrate  in  unison  with  it,  and  the  number  of  undu- 
lations in  the  path  traced  upon  the  cylinder  is  the 
number  of  vibrations  made.  By  this  ingenious  method 
the  number  of  vibrations  made  by  the  voice  in  singing, 
or  indeed  by  any  noise  whatever,  if  of  sufficient  inten 
sity,  may  be  directly  registered.  (Atkinson's  Ganot's 
Physics,  p.  190.) 

6.  The  electric  register. — The   electric  registf/r   [See 
(46.)  ]  may  give  a  direct  and  an  almost  unerring  registry 
of  the  vibrations  in  solid  or  liquid  bodies,  where  the 
amplitude  of  vibration  is  at  all  appreciable,  whether 
accompanied  by  sound  or  not. 

According  to  the  experiments  of  Wheatstone  the  pas- 


NATURAL    PHILOSOPHY.  299 

sage  of  the  electric  spark  in  the  discharge  of  the  Leyden- 
jar  occupies  24^00  of  a  second.  If  passed  through 
paper  moistened  with  iodide  of  potassium,  this  spark 
has  time  to  decompose  this  substance,  and  leave  a  brown 
stain  upon  the  paper.  When  a  little  starch  is  mixed 
with  the  iodide,  the  stain  is  blue  and  very  distinct. 
The  possibility  of  registering  at  least  24,000  double 
vibrations  a  second  is  thus  distinctly  pointed  out.  The 
requirements  are  :  1st,  a  steady  stream  of  electricity, 
from  a  powerful  battery ;  2d,  means  by  which  the 
motion  of  the  vibrating  body  may  open  and  close  this 
circuit ;  and  3d,  a  rapid  motion  of  the  chemically, 
prepared  paper,  through  which  the  electricity  is  passing. 
"With  an  apparatus  of  somewhat  rude  construction, 
applied  directly  to  the  wires  of  a  piano  in  daily  use, 
the  following  results  have  been  obtained. 

Note 0,   CJ,  D  ,  E&,  E  ,   F  ,  1$,    G,     A5,    A,     B5,      B,     O 

Vib.  per  See.  64.2,  67.1,  73.1,  76.1,  81.8,  87.1,  92.8,  98.1, 101.5, 107.8, 114.5, 117.5, 127.5. 

These  numbers  are  in  each  case  the  mean  of  several 
experiments,  but  in  no  set  of  experiments  did  the 
registry  vary  except  by  a  single  mark,  which  must  cor- 
respond to  an  error  of  less  than  one-half  a  vibration. 

The  C,  127.5,  is  written  in  the  second  space  of  the 
base. 


300  NATURAL    PHILOSOPHY. 


1L-LIGHT. 

(CHAPTER    VI.    CONTINUED), 
§    6.    INTERFERENCE    OF   LIGHT   AND   WAVE   LENGTHS. 

(108.)  LUMINOUS  vibrations,  by  crossing,  interfere, 
and  produce  waves  of  different  amplitude.  The  inten- 
sity of  light  depends  upon  the  amplitude  of  vibration ; 
its  color  upon  the  rapidity  of  vibration.  The  length  of 
waves  of  light  vary  from  .0000167  of  an  inch  to 
.0000266  of  an  inch.  Diffraction  fringes  are  the  effect 
of  interference. 

1.  The  interference  of  light. — We  have  learned 
that  light  is  th  e  result  of  vibrations  in  a  very  elastic 
medium  called  ether.  "We  ought,  therefore,  to  expect 
that  the  phenomena  of  light  would,  in  many  respects, 
be  like  those  of  sound  and  heat.  We  have  found  thia 
to  be  true,  their  laws  of  reflection,  refraction,  and  trans- 
mission being  alike.  They  are  alike  also  in  regard  to 
interference.  (See  Silliman's  Physics,  pp.  258  and 
273.) 

If  two  sound  waves  in  air  cross  each  other,  so  as  to 
bring  their  condensed  parts  or  phases  together,  they 
cause  a  wave  whose  amplitude  is  equal  to  the  sum  of 
theirs,  and  produce  a  sound  of  greater  intensity.  If 
they  come  together  in  such  way  that  the  condensed 
phase  of  one  strikes  the  rarefied  phase  of  the  other,  they 


NATURAL    PHILOSOPHY.  301 

cause  a  -wave  whose  amplitude  is  equal  to  the  difference 
of  theirs,  and  produce  a  sound  of  less  intensity. 

So,  too,  if  waves  of  light,  in  the  ether,  cross  each 
other  so  as  to  bring  their  like  phases  together,  they 
cause  a  wave  whose  amplitude  is  equal  to  the  sum  of 
theirs,  and  produce  a  light  of  greater  brightness ;  but 
if  their  opposite  phases  are  thrown  together,  they  form 
a  single  wave  whose  amplitude  is  equal  to  their  differ- 
ence, and  cause  a  light  of  less  intensity. 

Now,  examine  the  conditions  of  interference  more 
carefully.  A  wave  consists  of  two  phases,  and  the  sum 
of  their  lengths  is  the  length  of  the  wave.  Of  course, 
then,  each  phase  is  just  one  whole  wave  length  ahead  of 
the  next  one  behind  it  of  the  same  name,  and  just  one- 
half  a  wave  length  ahead  of  the  next  one  behind  it  of  a 
different  name.  If,  then,  two  sets  of  waves  are  to  in- 
terfere with  like  phases  together,  their  starting-pointa 
must  be  one  wave  length,  or  some  whole  number  of 
wave  lengths  apart ;  to  bring  different  phases  together, 
the  distance  between  their  starting-points  must  be  one- 
half  a  wave  length,  or  some  multiple  of  this. 

2.  Color  depends  upon  rapidity  of  vibration. — As 
the  pitch  of  sounds  depend  upon  the  rapidity  of  the 
vibrations  which  cause  them,  so  the  color  of  light  varies 
with  the  rapidity  of  luminous  vibrations.     A  red  light 
is  made  by  the  slowest,  a  violet  light  by  the  swiftest, 
vibrations. 

3.  The  length  of  light  waves. — Light  of  all   colon 
travels  with  the  same  velocity ;  and  since  violet  is  pro- 
duced by  the  most  rapid  vibrations,  the  length  of  ita 
waves  must  be  less  than  for  any  other.     Suppose,  now, 
that  two  sets  of  waves  start  from  surfaces  very  near  to 
each  other,  but  not  parallel :  at  some  points  the  dis 


302 


NATURAL    PHILOSOPHY. 


tance  between  them  will  correspond  to  the  wave  length 
for  violet ;  at  others,  to  the  wave  lengths  of  other  colors. 
The  result  of  the  interference  of  the  two  sets  of  wavea 
will  be  to  form,  at  different  points,  all  the  tints  of  the 
spectrum.  The  rainbow  colors  of  the  soap-bubble, 
which  so  delighted  us  in  childhood,  illustrate  this  most 
beautifully.  The  light  is  reflected  from  both  the  out- 
side and  the  inside  surfaces  of  the  thin  film ;  these  sur- 
faces are  not  parallel ;  and  the  interference  of  the  two 
sets  of  waves  gives  rise  to  the  colors. 

Now,  could  we  but  measure  the  thickness  of  the  film 
at  the  point  where  red  is  seen,  we  would  find  the  length 
of  the  wave  for  red ;  and  if  at  points  where  other  colors 
appear,  we  would  find  the  wave  lengths  which  produce 
them.  Newton  actually  calculated  these  minute  spaces, 
although,  of  course,  so  frail  a  thing  as  a  soap-bubble 
could  not  be  used  for  the  purpose.  His  plan  may  be 
understood  from  Fig.  143.  A  very  thin  layer  of  air  ia 

included  between  two 
very  smooth  glass  sur- 
faces, one  curved,  the 
other  plane.  When  the 
glasses  are  pressed  to- 
gether, a  series  of  rain- 
bow-colored rings  are 
seen,  with  a  black  cen- 
ter at  the  point  a, 
where  the  glasses  are  in 
contact.  If  red  light 
alone  is  used,  a  series 
of  red  rings  will  be  sep- 
arated by  dark  spaces. 
Now  these  rings  are  caused  by  the  interference  of 


NATURAL    PHILOSOPHY.  303 

two  sets  of  waves,  one  reflected  from  the  lower  side  of 
the  curved  glass,  the  other  from  the  upper  side  of  the 
plane  glass,  meeting  at  the  eye,  E.  JSTewton  calculated 
the  thickness  of  the  layer  of  air  at  points,  bode,  where 
the  rings  were  seen,  and  from  these  thicknesses  calcu- 
lated the  length  of  the  waves.  The  more  refrangible 
colors  are  produced  by  shorter  waves.  The  lengths  of 
luminous  waves  vary  between  .0000167  of  an  inch  for 
violet,  to  .0000266  of  an  inch  for  red.  (See  Silliman's 
Phys.,  p.  376.) 

4.  Diffraction. — Diffraction  is  the  change  which 
light  undergoes  when  it  passes  the  edge  of  an  opaque 
obstacle.  Place  two  knife-blades  edge  to  edge,  and 
look  through  the  narrow  slit  between  them  at  the  clear, 
bright  sky.  Instead  of  a  well-defined,  clear,  bright 
space,  a  great  number  of  very  delicate  parallel  black 
lines  will  be  seen.  The  edge  of  a  single  blade,  or  of 
any  thin  body,  will  appear  fringed  with  dark  lines, 
and,  under  some  circumstances,  with  colored  bands  of 
great  beauty.  One  who  has  been  taught  to  recognize 
it,  will  be  surprised  to  find  how  numerous  and  common 
are  the  various  forms  of  this  delicate  phenomenon.  A 
lady,  on  suddenly  lifting  her  eyes  to  the  bright  sky, 
sees  it,  through  the  meshes  of  her  veil,  covered  with  a 
net-work  of  rainbows.  Who  has  not  wondered  at  the 
brilliant  colors  of  the  sky,  seen  through  the  fine  fibers 
of  a  bird's  feather  ? 

By  the  following  experiment  diffraction  fringes  may 
be  shown  in  the  class-room.  A  beam  of  sunlight  L 
(Fig.  144),  coming  through  a  narrow  slit  in  the  shutter 
of  a  darkened  room,  is  made  to  pass  through  a  second 
slit  O,  at  a  distance  of  ten  or  fifteen  feet.  When  a 
white  screen,  S  (a  front  view  shown  at  S),  is  placed 


304  NATURAL    PHILOSOPHY. 

behind  this  slit,  at  a  distance  of  about  four  feet,  a  mul 
titude  of  colored  bands,  alternating  with  dark  spaces, 
will  appear  upon  it. 

Fig.  144. 


Diffraction  fringes  are  caused  by  the  interference  of 
light.  "When  one  set  of  waves  pass  an  obstacle,  it 
starts  another  set  in  the  ether  on  the  other  side.  These 
two  sets  going  almost,  but  not  exactly,  in  the  same  di- 
rection, interfere  and  give  rise  to  the  many  curious  re- 
sults known  as  diffraction. 

§  7.    DOUBLE   REFRACTION    AND    POLARIZATION. 

(109.)  When  a  beam  of  light  passes  through  a  crystal 
of  Iceland  spar  it  is  doubly  refracted.  The  two  beama 
which  emerge  ar,e  both  polarized.  Light  may  be  also 
polarized  by  reflection.  The  effects  of  polarized  light 
are  numerous  and  important. 

Fig.  146.  1.  Double  refraction. 

—Crystals  of  Iceland  spar 
are  found  very  trans- 
parent, and  of  a  form 
(Fig.  145)  as  regular  as 
could  be  cut  by  the  hand 
of  a  skillful  artist.  Each 
of  its  six  surfaces  is  a 
parallelogram.  They  are 
BO  arranged  that  three 


NATURAL    PHILOSOPHY.  3Q5 

of  them  have  eacli  an  obtuse  angle  at  A,  and  the  other 
three  each  an  obtuse  angle  at  B.  A  line  joining  the  points 
A  and  B  is  called  the  optic  axis  of  the  crystal.  Now, 
if  a  ray  of  light  be  passed  through  such  a  crystal  in 
any  direction  not  perpendicular  to  the  axis,  it  will 
emerge  as  two  separate  rays,  and  the  light  will  be  said 
to  be  doubly  refracted. 

Thus,  suppose  a  beam  of  light  coming  up  from  be- 
low enters  the  crystal  at  the  pointy  (Fig.  145),  it  will 
be  divided  into  two  parts,  o  and  0,  which,  emerging  at 
points  r  and  s,  go  on  as  parallel  and  separate  beams, 
and  cause  the  curious  effect  of  making  any  thing  on 
which  the  crystal  rests  appear  to  be  double.  One  of  these 
refracted  beams  (o)  obeys  the  regular  law  of  refraction ; 
the  other  (e)  does  not.  The  first  is  called  the  ordinary 
beam,  the  other  the  extraordinary  beam.  Many  other 
transparent  crystals  have  this  power  of  double  refrac- 
tion. 

2.  Both  beams  are  polarized. — A  very  curious  change 
is  wrought  in  the  light  by  double  refraction.  Com- 
mon light  will  pass  through  any  transparent  medium, 
no  matter  in  what  position  it  may  be  held,  but  these 
doubly  refracted  rays  are  able  to  pass  through  a  second 
medium  when  it  is  held  in  certain  positions  only.  For 
example,  if  the  ordinary  ray  be  made  to  fall  upon  a 
flat  plate  of  tourmaline  (a  transparent  mineral  crystal), 
and  it  go  through  when  in  one  position,  it  will  not  go 
through  when  the  plate  has  been  turned  90°  around. 
Turn  the  plate  90°  more,  and  the  ray  will  again  pass 
through  it ;  turn  it  90°  further  yet,  and  the  ray  will 
be  again  wholly  cut  off. 

If  the  extraordinary  ray  be  tried,  it  will  be  wholly 
transmitted  by  the  plate  in  positions  where  the  ordi 


306  NATURAL    PHILOSOPHY. 

nary  ray  was  cut  off,  and  wholly  cut  off  where  the 
other  was  transmitted. 

When  light,  by  being  refracted  or  reflected,  is  made 
incapable  of  being  again  refracted  or  reflected  except 
in  certain  directions,  it  is  said  to  be  polarized. 

3.  Polarization  by  reflection. — If  a  beam  of  light, 
shown  by  a  ~b  (Fig.  146),  falls  upon  a  plate  of  glass  at 
an   angle   of  in-  mg  146 

cidence    56|-0,   a 

part  of  it  will  pass 

into  the  glass,  the 

rest  of  it  will  be 

reflected.     If  the 

reflected  part  be 

examined    by    a 

plate  of  tourmaline  it  will  be  found  to  be  polarized. 

Or  if  another  plate  of  glass  !N",  is  placed   parallel  to 

the  first,  the  beam  will  be  reflected  as  the  figure  shows 

it,  but  let  the  plate  be  turned  90°,  as  showed  by  the 

dotted  lines,  and  the   beam  will   be  wholly  cut   off. 

Turn  it  90°  farther,  and  the  reflected  beam  appears 

again;  another  90°,  and  it  is  again  cut  off.     At  any 

other  angle  of  incidence  than  56^°,  the  light  will  be 

only  partly  polarized :  56J°  is  the  polarizing  angle  for 

glass. 

4.  Polarizing  instruments. — The  instruments,  called 
polariscopes,  by  which  to  study  polarized  light,  consists 
essentially  of  two  parts,  one  to  polarize  the  light,  the 
other  to  examine  it  after  it  has  been  polarized.     The 
lirst  is  called  the  polarizer,  the  second,  the  analyzer. 
One  of  the  simplest  forms  of  the  instrument  is  shown 
in  the  figure  (Fig.  147).     The  polarizer  P,  is  a  plate 
of  glass,  covered  on  the  back  of  it  with  black  varnish. 


NATURAL    PHILOSOPHY. 


307 


The  analyzer  A,  is  a  plate  of  tourmaline  set  into  a 
movaHe  tube.  Objects  to  be  examined  by  polarized 
light  are  supported  in  a  movable  ring  O. 


Fig.  14T. 


5.  Theory  of  polarization. — To  explain  the  phenom- 
ena of  polarization,  we  must  remember  that  light  is 
caused  by  vibrations,  and  add  to  this  the  assumption 
that  these  vibrations  take  place  in  all  possible  direc- 
tions at  right  angles  to  the  direction  in  which  the  ray 
itself  is  going.  Let  us  for  a  moment  suppose  that  we 
could  see  a  single  ray  of  light,  and  that  we  look  squarely 
at  the  end  of  it.  We  may  fancy  that  we  would  see  a 
circular  outline,  with  the  particles  of  ether  moving 
Bwiftly  in  the  directions  of  all  its  diameters.  Let  (Fig. 
148)  A  represent  this  view.  Now  the  theory  assumes 


that  by  refraction   or  reflection,  all  these  vibrations 
are  changed  into  two  sets,  one  which  vibrates  in  a 


308  NATURAL    PHILOSOPHY. 

horizontal  plane  (Fig.  148),  B,  and  the  other  in  a  vertical 
plane  (Fig.  148),  C.  This  change  is  what  is  called 
polarization.  The  tourmaline  plate,  or  the  plate  of 
glass,  will  let  one 'of  these  sets  of  vibrations  pass 
through  it  only  when  in  certain  positions,  owing  to 
some  peculiar  arrangement  of  its  molecules,  but  when  in 
position  to  cut  off  one  set  it  allows  the  other  to  pass  freely. 

6.  Effects  of  polarization. — When  a  thin  plate  of 
mica,  or  other  doubly  refracting  medium,  is  put  at  O,  in 
the  polariscope  (Fig.  147),  the  two  beams  emerging,  by 
interfering,  produce  most  beautiful  colors.  When  seen 
kin  certain  directions,  colored  rings  of  surprising  beauty, 
with  a  black  cross,  appear  (see  Atkinson's  Ganot's 
Phys.,  p.  510).  The  form  and  arrangement  of  these 
rings  differ  in  different  crystals — a  fact  of  much  interest 
to  the  mineralogist. 

Some  substances  have  the  power  to  change  the  posi- 
tion of  the  plane  of  vibration,  in  a  ray  of  polarized 
light.  Thus  if  the  analyzer  (Fig.  147),  is  turned  so  that 
the  ray  of  polarized  light  is  turned  off,  a  thin  plate  of 
quartz  at  O,  will  cause  the  ray  to  reappear.  In  this 
case  suppose  the  vibrations  to  be  in  the  vertical  plane, 
and  that  the  analyzer  is  turned  to  the  right  just  10° ; 
the  quartz  must  bend  the  plane  of  vibration  10°  to  the 
right  also,  in  order  that  the  ray  may  pass.  This  ia 
called  rotary  polarization. 

A  great  number  of  liquids  have  this  power.  Some 
of  them  turn  the  plane  to  the  right ;  such  is  a  solution 
of  cane  sugar ;  others  turn  the  plane  to  the  left ;  such 
is  a  solution  of  grape  sugar.  This  fact  is  of  great 
interest  to  the  chemist,  and  it  assists  the  physician  at 
*  times  to  determine  the  healthy  or  diseased  condition  of 
the  fluids  of  the  human  system. 


NATURAL    PHILOSOPHY.  309 


III.— HEAT. 

(CHAPTER  VII.   CONTINUED). 
§    5.   THE    MECHANICAL    EQUIVALENT    OF    HEAT.      . 

(110.)  As  MECHANICAL  action  produces  heat,  so  in 
disappearing,  heat  produces  mechanical  action.  The 
exchange  takes  place  in  definite  quantities.  The  force 
exerted  by  a  weight  of  772  Ibs.,  falling  through  a  dis- 
tance of  1  ft.,  produces  heat  enough  to  raise  the 
temperature  of  1  Ib.  of  water  1°  F. 

1.  Heat  lyy  mechanical  action. — We  have  seen  that 
friction,  percussion,  and  pressure,  are  sources  of  heat. 
Let  us  now  examine  these  sources  more  fully. 

When  two  pieces  of  wood  are  rubbed  togethe, ,  we 
notice  that  there  is,  1st,  the  force  of  the  hand,  2d,  the 
motion  of  the  pieces,  and  3d,  the  heat  evolved.  So, 
too,  when  one  body  strikes  another,  as  when  a  heavy 
weight  falls  upon  an  iron  plate,  we  may  notice,  1st,  the 
force  of  gravitation,  2d,  the  motion  of  the  weight,  and 
3d,  the  heat  produced  by  the  blow.  Should  we  ex- 
amine other  cases,  we  should  find  in  them  all,  as  in 
these,  that  mechanical  force  produces  motion,  and  that 
the  motion,  when  interrupted,  evolves  the  heat. 

2.  Mechanical  action  by  heat. — But  we  may  reverse 
the  order.     Heat,  by  producing  motion,  may  exert  me- 
chanical force.     The  steam-engine  affords  a  familiar 
and  sufficient  example.     In  this  machine,  the  heat  of 


310  NATURAL    PHILOSOPHY. 

the  furnace,  by  the  steam  it  forms,  gives  motion  to  the 
piston  by  which  the  tremendous  force  of  the  engine  is 
exerted.  Motion  is  the  medium  in  which  mechanical 
force  and  heat  are  interchanged. 

3.  In  the  exchange  no  loss  occurs. — The  motion  of  a 
sledge  hammer  can  give  rise  to  a  certain  amount  of 
motion  among  the  molecules  of  the  anvil  on  which  it 
falls,  -io  more,  no  less.     This  molecular  motion  appears 
as  heat.     Now,  if  this  heat  could  be  all  collected  and 
changed  back  into  mechanical  force,  it  would  be  just 
sufficient  to  lift  the  hammer  to  the  height  from  which 
it  fell.     The  amount  of  heat  produced  by  a  given  force 
will  always  be'the  same,  and  when  it  disappears  it  can 
exert  a  force  just  equal  to  that  which  caused  it.     Nature 
permits  no  loss  in  her  exchanges. 

4.  The  mechanical  equivalent  of  heat. — Is  it  then  pos- 
sible to  tell  just  how  much  heat  will  be  produced  by 
a  given  amount  of  mechanical  force,  or  how  much  force 
a  given  amount  of  heat  may  exert  if     This  has  been  done 
with  the  greatest  accuracy. 

The  first  step  in  the  investigation  was,  to  settle  upon 
Some  unit  by  which  to  measure  the  force  exerted,  and 
another  by  which  to  measure  the  heat  produced.  The 
unit  of  force  chosen,  is  the  force  exerted  by  a  weight 
of  1  lb.,  falling  a  distance  of  1  ft.  The  unit  of  heat,  is 
the  amount  of  heat  required  to  raise  the  temperature 
of  1  lb.  of  water  1°  F. 

Now  the  question  is,  how  many  units  of  force  will 
produce  one  unit  of  heat  ?  The  honor  of  first  answer- 
ing this  question  is  shared  by  Dr.  Mayer  of  Germany, 
and  Mr.  Joule  of  England,  who,  at  about  the  same 
time,  and  by  different  methods,  obtained  results  so 
much  alike  as  to  give  impartial  judges  great  confidence 


NATURAL    PHILOSOPHY. 

hi,  not  less  than  admiration  of,  the  labors  of  both.  The 
experiments  of  Joule  extended  through  seven  laborious 
years.  Dr.  Tyndall  thus  speaks  of  them  in  his  Heat  aa 
a  Mode  of  Motion : — 

"  He  placed  water  in  a  suitable  vessel,  and  agitated 
that  water  by  paddles  driven  by  forces  which  he  could 
measure,  and  determined  both  the  amount  of  heat,  by 
the  stirring  of  the  liquid,  and  the  amount  of  labor  ex- 
pended in  the  process.  He  did  the  same  with  mercury, 
and  with  sperm  oil.  He  also  caused  disks  of  cast-iron 
to  rub  against  each  other,  and  measured  the  heat  pro- 
duced by  their  friction,  and  the  force  expended  in  over- 
coming it.  He  also  urged  water  through  capillary 
tubes,  and  determined  the  amount  of  heat  generated 
by  the  friction  of  the  liquid  against  the  sides  of  the 
tubes.  And  the  results  of  his  experiments  leave  no 
shadow  of  a  doubt  upon  the  mind  that,  under  all  cir- 
cumstances the  quantity  of  heat  generated  by  the  same 
amount  of  force  is  fixed  and  invariable."  The  same 
author  goes  on  to  say:  "  It  was  found  that  the  quantity 
of  heat  which  would  raise  one  pound  of  water  one 
degree  Fahr.  in  temperature,  is  exactly  equal  to  what 
would  be  generated  if  a  pound  weight,  after  having 
fallen  through  a  height  of  772  ft.,  has  its  moving  force 
destroyed  by  collision  with  the  earth.  Conversely,  the 
amount  of  heat  necessary  to  raise  a  pound  of  water  one 
degree  in  temperature,  would,  if  all  applied  mechan- 
ically, be  competent  to  raise  a  pound  weight  772  feet 
Ligh,  or  it  would  raise  772  pounds  one  foot  high.  The 
term  'foot-pound'  has  been  introduced  to  express  the 
lifting  of  one  pound  to  the  height  of  a  foot."  Then 
772  foot-pounds  is  what  is  called  the  mechanical  equiva- 
lent of  heat. 


S12  NATURAL    PHILOSOPHT 


IV.— ELECTRICITY. 

(CHAPTER  VIII.  CONTINUED^. 

§  4:.    MAGNETO-ELECTRICITY. 

(111.)  Electricity  may  be  developed  by  a  magnet :  it 
is  then  called  magneto-electricity,  and  the  apparatus 
which  develops  it  is  called  a  magneto-electric  machine. 
All  the  effects  of  voltaic  electricity  may  be  caused  by 
electricity  from  a  magnet :  from  Wilde's  machine  these 
effects  are  most  extraordinary. 

1.  Magneto-electricity. — We  have  seen  that  when  a 
b&r  of  soft  iron   is  inclosed  in  a  coil  of  wire,  a  current 
of  electricity  renders  it  magnetic ;  now  just  reverse  the 
conditions :  put  a  magnet  into  a  coil,  and  a  current  of 
electricity  will  be  induced  in  the  wire.     It  flows  for  an 
instant  only,  but  is  renewed  when  the  magnet  is  with- 
drawn.    Or,  if  a  bar  of  soft  iron  be  rapidly  made  to 
receive  and  part  with  magnetism,  a  rapid  series  of  elec- 
tric currents  will  act  through  the  wire  which  is  wrapped 
around  it. 

2.  Magneto-electric  machine. — A  great  many  forms 
of  apparatus  for  getting  magneto-electricity  have  been 
devised :  one  of  the  most  common  is  shown  in  Fig. 
149.     In  this  instrument  two  coils  of  wire  (W)  inclose 
the  two  arms  of  a  bar  of  soft  iron,  having  the  form  of 
a  horseshoe  magnet,  and  which  by  a  band  and  wheel 
M,  can  be  put  in  rapid  motion  in  front  of  a  very  power- 


NATURAL    PHILOSOPHY. 


313 


fill  compound  magnet,  S.     The  soft  Jron  becomes  mag 
netic  whenever  its  ends  are  in  front  of  the  poles  of  the 
Dernmnent  magnet,  and,  hence,  its  two  branches   are 


Fig.  14». 


being  alternately  magnetized  in  opposite  states  at  every 
turn.  The  effect  of  this  is  to  produce  two  opposite 
currents  in  the  coils  at  every  revolution.  These  cur- 
rents are  taken  by  the  wires  <?,  and  thence  under  the 
instrument  to  the  screw  cups,  K  and  P. 

3.  Effects  of  magneto-electricity. — A  person  grasping 
the  handles  of  the  machine  (Fig.  149),  receives  shocks, 
which   become   unbearable  when   the   motion   of  the 
armature  is  rapid.      Chemical   decompositions,   heat, 
light,  and  indeed  all  the  effects  of  electricity  from  a 
voltaic  battery,  may  be  obtained   by  magneto- elec- 
tricity. 

4.  Wilde^  machine. — The  electricity  obtained  from 
the  machine  (Fig.  149),  may  be  used  to  magnetize  an 
electro-magnet,  and  an  armature  revolving  in  front  of 
its  poles   will   give   a  powerful   current,   by  which   a 
second  and  still  stronger  electro-magnet  may  be  mag- 

u 


314  NATURAL     PHILOSOPHY. 

netized.  Upon  this  principle,  Mr.  Wilde,  of  England, 
has  invented  a  machine  of  great  power.  Starting  with 
several  strong  steel  magnets  in  a  row,  electricity  is 
is  taken  from  the  wire  of  a  long  armature  revolving  be- 
tween their  poles,  and  passed  through  the  coil  of  a  very 
large  electro-magnet.  From  another  armature,  revolv- 
ing between  the  poles  of  this  magnet,  a  second  current 
of  electricity,  some  hundreds  of  times  stronger  than  the 
first,  is  taken,  and  used  for  any  purpose  for  which  the 
machine  is  intended.  The  armatures  are  turned  by  a 
steam-engine. 

The  most  extraordinary  effects  are  produced  by  this 
machine.  With  a  small  one,  having  only  six  smaL 
steel  magnets,  an  iron  rod,  fifteen  inches  long,  and  a 
quarter  of  an  inch  in  diameter,  was  melted,  and  in  the 
light  produced  by  a  larger  machine,  the  flames  of  street 
lamps  half  a  mile  away,  were  said  to  have  cast  shadow* 
upon  a  screen. 

§    5.    THERMO-ELEOTKIOTTY. 

(112.)  Electricity  may  be  developed  by  heat :  it  i§ 
then  called  thermo  electricity. 

1 .  Thermo-electricity. — We  have  seen  that  electricity 
will  produce  heat;  we  are  now  to  notice  that  heat  will 
produce  electricity.  When  two  pieces  of  different 
metals  are  soldered  together,  and  their  junction  heated 
or  cooled,  a  current  of  electricity  is  produced.  The 
metals  antimony  and  bismuth  are  best  suited  to  this 
purpose,  but  any  others,  or  indeed,  two  pieces  of  the 
same  metal,  will,  in  some  degree,  produce  the  same 
effect.  Nor  is  it  quite  necessary  that  metals  should  be 


NATURAL    PHILOSOPHY.  31fi 

used  at  all ;  other  solids,  and  even  fluids,  give  rise  to 
this  kind  of  electricity. 

Two  pieces  of  metal  soldered  together,  with  wires 
attached  to  their  other  ends,  through  which  the  elec- 
tricity may  act,  is  called  a  thermo-electric  pair.  When 
Stronger  currents  are  desired,  a  combination  of  pairs, 
the  two  metals  alternating  throughout,  is  used.  Such 
a  combination  is  called  a  thermo-electric  pile. 

Metals  which  differ  most  in  conducting  power  and 
crystalline  texture,  are  best  suited  to  produce  thermo- 
electric currents.  The  force  of  the  electricity  is  in  pro- 
portion to  the  difference  of  temperature  at  the  two 
ends  of  the  pile,  provided  the  difference  does  not 
exceed  80°  or  90°  F.  It  is  in  all  cases  very  feeble ;  yet 
the  galvanometer  (an  astatic  needle  inclosed  in  a  helix) 
responds  to  so  delicate  a  force,  that  the  slightest  change 
of  temperature  in  the  pile  can  be  detected  by  the  cur- 
rent it  produces.  Indeed  the  thermo-electric  pile  and 
galvanometer  (Melloni's  apparatus),  is  the  most  delicate 
thermometer  known.  (See  Silliman's  Phy8.,  pp.  636 
and  443.) 


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